Я. Г. Синай, “Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов”, УМН, 25:2(152) (1970), 141–192; Russian Math. Surveys, 25:2 (1970), 137

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УМН, 1970, том 25, выпуск 2(152), страницы 141–192 (Mi umn5322)

Эта публикация цитируется в 512 научных статьях (всего в 516 статьях)

Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов

Я. Г. Синай

Аннотация: В статье рассматриваются динамические системы, порожденные движением материальной точки в областях со строго выпуклым внутрь краем, т. е. в таких, что оператор второй квадратичной формы в каждой точке границы области отрицательно определенный, если считать край оснащенным полем внутренних нормалей. Доказывается, что такие системы эргодичныи являются $K$-системами. В основе метода исследования лежит построение трансверсальных слоений для таких систем и изучение свойств этих слоений.

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Англоязычная версия:
Russian Mathematical Surveys, 1970, 25:2, 137–189

Реферативные базы данных:

УДК: 518.25
MSC: 37N05, 37Axx, 37D50, 37D40
Поступила в редакцию: 11.12.1969

Образец цитирования: Я. Г. Синай, “Динамические системы с упругими отражениями. Эргодические свойства рассеивающих бильярдов”, УМН, 25:2(152) (1970), 141–192; Russian Math. Surveys, 25:2 (1970), 137–189

Цитирование в формате AMSBIB

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\by Я.~Г.~Синай

\paper Динамические системы с~упругими отражениями. Эргодические

свойства рассеивающих бильярдов

\jour УМН

\yr 1970

\vol 25

\issue 2(152)

\pages 141--192

\mathnet{http://mi.mathnet.ru/umn5322}

\mathscinet{http://www.ams.org/mathscinet-getitem?mr=274721}

\zmath{https://zbmath.org/?q=an:0252.58005|0263.58011}

\transl

\jour Russian Math. Surveys

\yr 1970

\vol 25

\issue 2

\pages 137--189

\crossref{https://doi.org/10.1070/RM1970v025n02ABEH003794}

Образцы ссылок на эту страницу:

http://mi.mathnet.ru/umn5322

http://mi.mathnet.ru/rus/umn/v25/i2/p141

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Эта публикация цитируется в следующих статьяx:

Stoddard S.D., Ford J., “Numerical experiments on the stochastic behavior of a Lennard-Jones gas system”, Phys. Rev. A, 8:3 (1973), 1504–1512
Л. А. Бунимович, Я. Г. Синай, “Об основной теореме теории рассеивающих бильярдов”, Матем. сб., 90(132):3 (1973), 415–431 ; L. A. Bunimovich, Ya. G. Sinai, “On a fundamental theorem in the theory of dispersing billiards”, Math. USSR-Sb., 19:3 (1973), 407–423
J.L.. Lebowitz, Oliver Penrose, “Modern ergodic theory”, Phys. Today, 26:2 (1973), 23
А. И. Шнирельман, “Эргодические свойства собственных функций”, УМН, 29:6(180) (1974), 181–182
Л. А. Бунимович, “О бильярдах, близких к рассеивающим”, Матем. сб., 94(136):1(5) (1974), 49–73 ; L. A. Bunimovich, “On billiards close to dispersing”, Math. USSR-Sb., 23:1 (1974), 45–67
D.B. Abraham, D.J. Gates, “Models for a high-density phenomenon in the Lorentz gas”, Physica, 72:1 (1974), 73
Goldstein Sh., “Space-time ergodic properties of systems of infinitely many independent particles”, Comm. Math. Phys., 39:4 (1975), 303–327
Giulio Casati, Joseph Ford, “Computer study of ergodicity and mixing in a two-particle, hard point gas system”, Journal of Computational Physics, 20:1 (1976), 97
М. Войтковски, “Символическая динамика в одной бильярдной задаче”, УМН, 32:3(195) (1977), 153–154
Я. Б. Песин, “Характеристические показатели Ляпунова и гладкая эргодическая теория”, УМН, 32:4(196) (1977), 55–112 ; Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114
K.-i. Nakamura, “Nonlinear Fluctuations Associated with Instabilities in Dissipative Systems”, Progress of Theoretical Physics, 57:6 (1977), 1874
Mangel M., “Fluctuations at chemical instabilities”, J. Chem. Phys., 69:8 (1978), 3697–3708
K.-i. Nakamura, “Numerical Experiments on Trajectory Instabilities in Dissipative Systems”, Progress of Theoretical Physics, 59:1 (1978), 64
Mangel M., “Small fluctuations in systems with multiple steady states”, SIAM J. Appl. Math., 36:3 (1979), 544–572
Я. Г. Синай, “Эргодические свойства газа Лоренца”, Функц. анализ и его прил., 13:3 (1979), 46–59 ; Ya. G. Sinai, “Ergodic properties of the Lorentz gas”, Funct. Anal. Appl., 13:3 (1979), 192–202
Marc Mangel, “Uniform treatment of fluctuations at critical points”, Physica A: Statistical Mechanics and its Applications, 97:3 (1979), 597
Spohn H., “Kinetic equations from Hamiltonian dynamics: Markovian limits”, Rev. Mod. Phys., 52:3 (1980), 569–615
Bunimovich L.A., Sinai Ya.G., “Markov Partitions for dispersed billiards”, Comm. Math. Phys., 78:2 (1980), 247–280
Berry M.V., “Quantization of mappings and other simple classical models”, Nonlinear dynamics (New York, 1979), Ann. N.Y. Acad. Sci., 357, no. 1, 1980, 183–202
Smale S., “On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff”, Nonlinear dynamics (New York, 1979), Ann. N.Y. Acad. Sci., 357, no. 1, 1980, 260
Berry M.V., “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular “billiard””, European J. Phys., 2:2 (1981), 91–102
К. М. Ефимов, “Эргодические свойства взаимодействующего газа Лоренца”, УМН, 36:6(222) (1981), 215–216 ; K. M. Efimov, “Ergodic properties of an interacting Lorentz gas”, Russian Math. Surveys, 36:6 (1981), 173–174
M.V. Berry, “Quantizing a classically ergodic system: Sinai's billiard and the KKR method”, Annals of Physics, 131:1 (1981), 163
P.J. Richens, M.V. Berry, “Pseudointegrable systems in classical and quantum mechanics”, Physica D: Nonlinear Phenomena, 2:3 (1981), 495
G.M.. Zaslavsky, “Stochasticity in quantum systems”, Physics Reports, 80:3 (1981), 157
van Beijeren H., “Transport properties of stochastic Lorentz models”, Rev. Modern Phys., 54:1 (1982), 195–234
Fucito F., Marchesoni F., Marinari E., Parisi G., Peliti L., Ruffo S., Vulpiani A., “Approach to equilibrium in a chain of nonlinear oscillators”, J. Physique, 43:5 (1982), 707–713
Н. И. Чернов, “Построение трансверсальных слоев в многомерных полурассеивающих бильярдах”, Функц. анализ и его прил., 16:4 (1982), 35–46 ; N. I. Chernov, “Structure of transversal leaves in multidimensional semidispersing billiards”, Funct. Anal. Appl., 16:4 (1982), 270–280
Barrow J.D., “Chaotic behaviour in general relativity”, Physics Reports, 85:1 (1982), 1–49
N Saitô, H Hirooka, J Ford, F Vivaldi, G.H Walker, “Numerical study of billiard motion in an annulus bounded by non-concentric circles”, Physica D: Nonlinear Phenomena, 5:2-3 (1982), 273
Toshiki Matsushita, Akira Narita, Toshikata Terasaka, “Chaotic behavior of a classical coupled morse system around the escape energy region”, Chemical Physics Letters, 95:2 (1983), 129
Mario Feingold, Asher Peres, “Regular and chaotic motion of coupled rotators”, Physica D: Nonlinear Phenomena, 9:3 (1983), 433
J. Iturbe, S.L. Allman, G.S. Hurst, M.G. Payne, “Time- and space-summation studies of the diffusion equation: experimental test of the ergodic hypothesis”, Chemical Physics Letters, 94:5 (1983), 505
Friedman B., Oono Y., Kubo I., “Universal behavior of Sinai billiard systems in the small-scatterer limit”, Phys. Rev. Lett., 52:9 (1984), 709–712
Б. В. Медведев, “Динамическая стохастичность и квантование”, ТМФ, 60:2 (1984), 224–244 ; B. V. Medvedev, “Dynamic stochasticity and quantization”, Theoret. and Math. Phys., 60:2 (1984), 782–797
K. M. Efimov, “The central limit theorem for the Lorentz gas and martingales”, Stochastics, 14:1 (1984), 1
Ishikawa T., Yukawa T., “Transition from regular to irregular spectra in quantum billiards”, Phys. Rev. Lett., 54:15 (1985), 1617–1619
Lech PapieŻ, “Consequences of the dynamical approach to the nuclear spin relaxation induced by molecular rotations in an external magnetic field”, Physics Letters A, 107:9 (1985), 438
Wojtkowski M., “Principles for the design of billiards with nonvanishing Lyapunov exponents”, Comm. Math. Phys., 105:3 (1986), 391–414
Nicolis G., “Dissipative systems”, Rep. Prog. Phys., 49:8 (1986), 873–949
Bouchard J., Le Doussal P., “Critical behaviour and intermittency in Sinai's billiard”, Physica D: Nonlinear Phenomena, 20:2-3 (1986), 335–349
A. Zacherl, T. Geisel, J. Nierwetberg, G. Radons, “Power spectra for anomalous diffusion in the extended Sinai billiard”, Physics Letters A, 114:6 (1986), 317
A. Ramani, A. Kalliterakis, B. Grammaticos, B. Dorizzi, “Integrable curvilinear billiards”, Physics Letters A, 115:1-2 (1986), 25
Eugene Gutkin, “Billiards in polygons”, Physica D: Nonlinear Phenomena, 19:3 (1986), 311
Reichl L.E., Lin W.A., “The search for a quantum KAM theorem”, Found. Phys., 17:7 (1987), 689–697
Brown R., Ott E., Grebogi C., “Ergodic adiabatic invariants of chaotic systems”, Phys. Rev. Lett., 59:11 (1987), 1173–1176
Wilkinson M., “A semiclassical sum rule for matrix elements of classically chaotic systems”, J. Phys. A, 20:9 (1987), 2415–2423
Я. Г. Синай, Н. И. Чернов, “Эргодические свойства некоторых систем двумерных дисков и трехмерных шаров”, УМН, 42:3(255) (1987), 153–174 ; Ya. G. Sinai, N. I. Chernov, “Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls”, Russian Math. Surveys, 42:3 (1987), 181–207
M Baranger, K.T.R Davies, “Periodic trajectories for a two-dimensional nonintegrable Hamiltonian”, Annals of Physics, 177:2 (1987), 330
M. Paramio, J. Sesma, “Breakdown of KAM tori in the standard map”, Physics Letters A, 124:6-7 (1987), 345
Bleher S., Grebogi C., Ott E., Brown R., “Fractal boundaries for exit in Hamiltonian dynamics”, Phys. Rev. A, 38:2 (1988), 930–938
Fairlie D.B., Siegwart D.K., “Classical billiards in a rotating boundary”, J. Phys. A, 21:5 (1988), 1157–1165
Chang Shau-Jin, Friedberg R., “Elliptical billiards and Poncelet's theorem”, J. Math. Phys., 29:7 (1988), 1537–1550
Wojtkowski M.P., “Measure theoretic entropy of the system of hard spheres”, Ergodic Theory Dynam. Systems, 8:1 (1988), 133–153
B. Friedman, R.F. Martin, “Behavior of the velocity autocorrelation function for the periodic Lorentz gas”, Physica D: Nonlinear Phenomena, 30:1-2 (1988), 219
P.R. Baldwin, “Soft billiard systems”, Physica D: Nonlinear Phenomena, 29:3 (1988), 321
J.C. Kimball, H.L. Frisch, “Channeling and the periodic Lorentz gas”, Physics Letters A, 128:5 (1988), 273
Stojanov L., “An estimate from above of the number of periodic orbits for semi-dispersed billiards”, Comm. Math. Phys., 124:2 (1989), 217–227
Mistriotis A.D., “A study on the short time dynamical behavior of Hamiltonian systems and its relationship to non-equilibrium statistical properties”, Phys. Scr., 39:1 (1989), 33–39
Chang Shau-Jin, Shi Kang-Jie, “Billiard systems on quadric surfaces and the Poncelet theorem”, J. Math. Phys., 30:4 (1989), 798–804
В. А. Малышев, Я. Г. Синай, “О некоторых работах по эргодической теории и математическим проблемам статистической механики на кафедре теории вероятностей МГУ”, ТВП, 34:1 (1989), 215–222 ; V. A. Malyshev, Ya. G. Sinai, “Some works on ergodic theory and mathematical problems of statistical mechanics at the Department of Probability Theory of Moscow State University”, Theory Probab. Appl., 34:1 (1989), 186–193
Simányi N., Wojtkowski M.P., “Two-particle billiard system with arbitrary mass ratio”, Ergodic Theory Dynam. Systems, 9:1 (1989), 165–171
Thirumalai D., Kirkpatrick T.R., “Ergodic behavior in supercooled liquids and in glasses”, Phys. Rev. A, 39:7 (1989), 3563–3574
Mackey M.C., “The dynamic origin of increasing entropy”, Rev. Mod. Phys., 61:4 (1989), 981–1015
Cheon T., Cohen Th.D., “Quantum level statistics of pseudointegrable billiards”, Phys. Rev. Lett., 62:24 (1989), 2769–2772
Krámli A., Simányi N., Szász D., “Dispersing billiards without focal points on surfaces are ergodic”, Comm. Math. Phys., 125:3 (1989), 439–457
Siegwart D.K., J. Phys. A, 22:17 (1989), 3537–3550
Б. В. Медведев, “Динамическая стохастичность и интегралы движения”, ТМФ, 79:3 (1989), 404–415 ; B. V. Medvedev, “Dynamic stochasticity and integrals of the motion”, Theoret. and Math. Phys., 79:3 (1989), 618–627
Friedrich H., Wintgen H., “The hydrogen atom in a uniform magnetic field — An example of chaos”, Physics Reports, 183:2 (1989), 37–79
S Adachi, “A numerical evaluation of the semiclassical coherent state path integral”, Annals of Physics, 195:1 (1989), 45
Bauer W., Bertsch G.F., “Decay of ordered and chaotic systems”, Phys. Rev. Lett., 65:18 (1990), 2213–2216
Dahlqvist P., Russberg G., “Existence of stable orbits in the $x^2y^2$ potential”, Phys. Rev. Lett., 65:23 (1990), 2837–2838
Stolovitzky G., Hernando J.A., “Attractive and repulsive interactions in a two-dimensional billiardlike system: The Lennard-Jones stadium”, Phys. Rev. A, 41:12 (1990), 6716–6726
Wojtkowski M.P., “Linearly stable orbits in 3 dimensional billiards”, Comm. Math. Phys., 129:2 (1990), 319–327
Wojtkowski M.P., “A system of one dimensional balls with gravity”, Comm. Math. Phys., 126:3 (1990), 507–533
Hannay J.H., McCraw R.J., “Barrier billiards—a simple pseudo-integrable system”, J. Phys. A, 23:6 (1990), 887–899
Sěba P., “Wave chaos in singular quantum billiard”, Phys. Rev. Lett., 64:16 (1990), 1855–1858
Troubetzkoy S.E., “A comparison of elastic and inelastic billiards”, Nonlinearity, 3:3 (1990), 947–960
Л. А. Бунимович, Я. Г. Синай, Н. И. Чернов, “Марковские разбиения для двумерных гиперболических биллиардов”, УМН, 45:3(273) (1990), 97–134 ; L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Markov partitions for two-dimensional hyperbolic billiards”, Russian Math. Surveys, 45:3 (1990), 105–152
И. В. Кривошей, “Критерий неустойчивости в многомерных нелинейных гамильтоновых системах”, ТМФ, 82:2 (1990), 268–277 ; I. V. Krivoshei, “Instability criterion for multidimensional nonlinear Hamiltonian systems”, Theoret. and Math. Phys., 82:2 (1990), 187–194
Izrailev F.M., “Simple models of quantum chaos: Spectrum and eigenfunctions”, Physics Reports, 196:5-6 (1990), 299–392
Bouchaud J.-Ph., Georges A., “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications”, Physics Reports, 195:4-5 (1990), 127–293
Alexander P. Veselov, “Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space”, Journal of Geometry and Physics, 7:1 (1990), 81
Šeba P., Życzkowski K., “Wave chaos in quantized classically nonchaotic systems”, Phys. Rev. A, 44:6 (1991), 3457–3465
Bunimovich L.A., “Conditions of stochasticity of two-dimensional billiards”, Chaos, 1:2 (1991), 187–193
Donnay V., Liverani C., “Potentials on the two-torus for which the Hamiltonian flow is ergodic”, Comm. Math. Phys., 135:2 (1991), 267–302
Donnay V.J., “Using integrability to produce chaos: Billiards with positive entropy”, Comm. Math. Phys., 141:2 (1991), 225–257
Baldwin P.R., J. Phys. A, 24:16 (1991), L941–L947
Eloranta K., “Alpha-congruence for dispersive billiards”, Ergodic Theory Dynam. Systems, 11:2 (1991), 309–331
Csordás A., Graham R., “Level statistics of a noncompact cosmological billiard”, Phys. Rev. A, 44:3 (1991), 1491–1499
Graham R., Hübner R., Szépfalusy P., Vattay G., “Level statistics of a noncompact integrable billiard”, Phys. Rev. A, 44:11 (1991), 7002–7015
Arve P., “Time scales of ergodic classical dynamics in quantal spectra”, Phys. Rev. A, 44:10 (1991), 6920–6922
Н. И. Чернов, “Топологическая энтропия и периодические точки двумерных гиперболических биллиардов”, Функц. анализ и его прил., 25:1 (1991), 50–57 ; N. I. Chernov, “Topological entropy and periodic points of two-dimensional hyperbolic billiards”, Funct. Anal. Appl., 25:1 (1991), 39–45
Н. И. Чернов, “Новое доказательство формулы Синая для вычисления энтропии гиперболических биллиардов. Приложение к газу Лоренца и стадиону Бунимовича”, Функц. анализ и его прил., 25:3 (1991), 50–69 ; N. I. Chernov, “New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums”, Funct. Anal. Appl., 25:3 (1991), 204–219
И. К. Бабенко, “О поведении траекторий рассеивающих бильярдов на плоском торе”, Матем. сб., 182:2 (1991), 220–235 ; I. K. Babenko, “On the behavior of trajectories of scattering billiards on the flat torus”, Math. USSR-Sb., 72:1 (1992), 207–220
Л. А. Бунимович, Я. Г. Синай, Н. И. Чернов, “Статистические свойства двумерных гиперболических биллиардов”, УМН, 46:4(280) (1991), 43–92 ; L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Statistical properties of two-dimensional hyperbolic billiards”, Russian Math. Surveys, 46:4 (1991), 47–106
С. Е. Трубецкой, “Стохастическая устойчивость рассеивающих бильярдов”, ТМФ, 86:2 (1991), 221–230 ; S. E. Trubetskoi, “Stochastic stability of dispersing billiards”, Theoret. and Math. Phys., 86:2 (1991), 151–158
Alessandro Monge, “The phenomenon of diverging phase-space trajectories for a class of Hamiltonian maps”, Physics Letters A, 153:4-5 (1991), 204
Nikolai I. Chernov, “The ergodicity of a Hamiltonian system of two particles in an external field”, Physica D: Nonlinear Phenomena, 53:2-4 (1991), 233
Isichenko M.B., “Percolation, statistical topography, and transport in random media”, Rev. Modern Phys., 64:4 (1992), 961–1043
Wang X.-J., “Dynamical sporadicity and anomalous diffusion in the Lévy motion”, Phys. Rev. A, 45:12 (1992), 8407–8417
Biham O., Kvale M., “Unstable periodic orbits in the stadium billiard”, Phys. Rev. A, 46:10 (1992), 6334–6339
Markarian R., “Ergodic properties of plane billiards with symmetric potentials”, Comm. Math. Phys., 145:3 (1992), 435–446
Bunimovich L., Liverani C., Pellegrinotti A., Suhov Yu., “Ergodic systems of $n$ balls in a billiard table”, Comm. Math. Phys., 146:2 (1992), 357–396
Chernov N., Markarian R., “Entropy of non-uniformly hyperbolic plane billiards”, Bol. Soc. Brasil. Mat. (N.S.), 23:1-2 (1992), 121–135
Biswas D., Azam M., Lawande Q.V., Lawande S.V., “Existence of stable periodic orbits in the $x^2y^2$ potential: a semiclassical approach”, J. Phys. A, 25:7 (1992), L297–L301
Harayama T., Shudo A., “Periodic orbits and semiclassical quantization of dispersing billiards”, J. Phys. A, 25:17 (1992), 4595–4611
Dahlqvist P., “Semiclassical mechanics of bound chaotic potentials”, Chaos, 2:1 (1992), 43–52
Dahlqvist P., “Influence of intermittency on quantum spectra”, J. Phys. A, 25:23 (1992), 6265–6282
Mortessagne F., Legrand O., Sornette D., “Renormalization of exponential-decay rates by fluctuations of barrier encounters”, Europhys. Lett., 20:4 (1992), 287–293
James Chen, “Nonlinear dynamics of charged particles in the magnetotail”, J. Geophys. Res, 97:A10 (1992), 15011
Jarzynski C., “Energy diffusion in a chaotic adiabatic billiard gas”, Phys. Rev. E, 48:6 (1993), 4340–4350
Lue A., Brenner H., “Phase flow and statistical structure of Galton-board systems”, Phys. Rev. E, 47:5 (1993), 3128–3144
Chernov N.I., Eyink G.L., Lebowitz J.L., Sinai Ya.G., “Steady-state electrical conduction in the periodic Lorentz gas”, Comm. Math. Phys., 154:3 (1993), 569–601
Tsai Yan-Chr, Shapir Y., “On the scale-invariant distribution of the diffusion coefficient for classical particles diffusing in disordered media”, J. Phys. A, 26:1 (1993), 39–50
Markarian R., “New ergodic billiards: exact results”, Nonlinearity, 6:5 (1993), 819–841
Dietz B., Smilansky U., “A scattering approach to the quantization of billiards—the inside-outside duality”, Chaos, 3:4 (1993), 581–589
Mortessagne F., Legrand O., Sornette D., “Transient chaos in room acoustics”, Chaos, 3:4 (1993), 529–541
Crespi B., Perez G., Chang Shau-Jin, “Quantum Poincaré sections for two-dimensional billiards”, Phys. Rev. E, 47:2 (1993), 986–991
Ackland G.J., “Equipartition and ergodicity in closed one-dimensional systems of hard spheres with different masses”, Phys. Rev. E, 47:5 (1993), 3268–3275
Chang Shau-Jin, Crespi B., Shi Kang-Jie, “Elliptical billiard systems and the full Poncelet's theorem in $n$ dimensions”, J. Math. Phys., 34:6 (1993), 2242–2256
U. Smilansky, “On hearing the shape of a drum, and related problems”, Contemporary Physics, 34:6 (1993), 297
Uzy Smilansky, “A zeta function approach to the semiclassical quantization of maps”, Nuclear Physics A, 560:1 (1993), 57
Igor V. Lerner, “Distributions of the diffusion coefficient for the quantum and classical diffusion in disordered media”, Nuclear Physics A, 560:1 (1993), 274
T. Dagaeff, C. Rouvinez, “On the discontinuities of the boundary in billiards”, Physica D: Nonlinear Phenomena, 67:1-3 (1993), 166
Nobuhiko Saitô, Akira Shudo, “Ergodicity, Irreversibility and Approach to Equilibrium”, J. Phys. Soc. Jpn, 62:1 (1993), 53
Garrido P.L., Gallavotti G., “Billiards correlation functions”, J. Statist. Phys., 76:1-2 (1994), 549–585
Chernov N.I., “Statistical properties of the periodic Lorentz gas. Multidimensional case”, J. Statist. Phys., 74:1-2 (1994), 11–53
Boasman P.A., Smilansky U., “Quantization of monotonic twist maps”, J. Phys. A, 27:4 (1994), 1373–1385
Bauer W., McGrew D., Zelevinsky V., Schuck P., “Coexistence of regular undamped nuclear dynamics with intrinsic chaoticity”, Phys. Rev. Lett., 72:24 (1994), 3771–3774
Srednicki M., “Chaos and quantum thermalization”, Phys. Rev. E, 50:2 (1994), 888–901
Emch G.G., Narnhofer H., Thirring W., Sewell G.L., “Anosov actions on noncommutative algebras”, J. Math. Phys., 35:11 (1994), 5582–5599
Isichenko M.B., Gruzinov A.V., “Isotopological relaxation, coherent structures, and Gaussian turbulence in two-dimensional (2-D) magnetohydrodynamics (MHD)”, Phys. Plasmas, 1:6 (1994), 1802–1816
Morita T., “Periodic orbits of a dynamical system in a compound central field and a perturbed billiards system”, Ergodic Theory Dynam. Systems, 14:3 (1994), 599–619
von Oppen F., “Magnetic susceptibility of ballistic microstructures”, Phys. Rev. B, 50:23 (1994), 17151–17161
Fendrik A.J., Rivas A.M.F., Sánchez M.J., “Decay of quasibounded classical Hamiltonian systems and their internal dynamics”, Phys. Rev. E, 50:3 (1994), 1948–1958
Mucciolo E.R., Capaz R.B., Altshuler B.L., Joannopoulos J.D., “Manifestation of quantum chaos in electronic band structures”, Phys. Rev. B, 50:12 (1994), 8245–8251
Davies P.A., “Edge-ray principle of nonimaging optics”, J. Opt. Soc. Amer. A, 11:4 (1994), 1256–1259
К. М. Ефимов, “Теорема типа Лифшица для рассеивающих биллиардов”, ТМФ, 98:2 (1994), 184–196 ; K. M. Efimov, “Theorem of Livšic type for dispersed billiards”, Theoret. and Math. Phys., 98:2 (1994), 122–131
Otto E. Rossler, “Micro constructivism”, Physica D: Nonlinear Phenomena, 75:1-3 (1994), 438
Maciej P. Wojtkowski, “The system of two spinning disks in the torus”, Physica D: Nonlinear Phenomena, 71:4 (1994), 430
Zheng Zhigang, Hu Gang, Zhang Juyuan, “Ergodic property of a Henon-Heiles model with reflecting walls”, Phys. Rev. E, 52:4 (1995), 3440–3446
Gaspard P., Dorfman J.R., “Chaotic scattering theory, thermodynamic formalism, and transport coefficients”, Phys. Rev. E, 52:4, part A (1995), 3525–3552
Dellago Ch., Posch H.A., “Lyapunov exponents of systems with elastic hard collisions”, Phys. Rev. E, 52:3, part A (1995), 2401–2406
Balazs N.L., Chatterjee R., Jackson A.D., “Coin tossing as a billiard problem”, Phys. Rev. E, 52:4 (1995), 3608–3613
Bäcker A., Steiner F., Stifter P., “Spectral statistics in the quantized cardioid billiard”, Phys. Rev. E, 52:3 (1995), 2463–2472
Gallavotti G., Cohen E.G.D., “Dynamical ensembles in nonequilibrium statistical mechanics”, Phys. Rev. Lett., 74:14 (1995), 2694–2697
Srednicki M., “Quantum chaos and statistical mechanics”, Ann. N.Y. Acad. Sci., 755:1, Fundamental Problems in Quantum Theory (1995), 757–760
Gallavotti G., Cohen E.G.D., “Dynamical ensembles in stationary states”, J. Statist. Phys., 80:5-6 (1995), 931–970
Markarian R., “Statistical properties of dynamical systems with singularities”, J. Statist. Phys., 80:5-6 (1995), 1207–1239
Morriss G.P., Rondoni L., Cohen E.G.D., “A dynamical partition function for the Lorentz gas”, J. Statist. Phys., 80:1-2 (1995), 35–43
Chernov N.I., “Limit theorems and Markov approximations for chaotic dynamical systems”, Probab. Theory Related Fields, 101:3 (1995), 321–362
Fendrik A.J., Sánchez M.J., “Decay of quasi-bounded classical Hamiltonian systems populated by scattering experiments”, J. Phys. A, 28:15 (1995), 4235–4243
Dahlqvist P., “Approximate zeta functions for the Sinai billiard and related systems”, Nonlinearity, 8:1 (1995), 11–28
Jarzynski C., “Thermalization of a Brownian particle via coupling to low-dimensional chaos”, Phys. Rev. Lett., 74:15 (1995), 2937–2940
Bunimovich L.A., “Variational principle for periodic trajectories of hyperbolic billiards”, Chaos, 5:2 (1995), 349–355
Fendrik A.J., Sánchez M.J., “Decay of the Sinai well in $D$ dimensions”, Phys. Rev. E, 51:4 (1995), 2996–3001
Román F.L., White J.A., Velasco S., “Single-particle distributions for small hard particle systems in the microcanonical and in the molecular-dynamics ensembles”, Phys. Rev. E, 51:6 (1995), 6271–6274
Artuso R., Casati G., Guarneri I., “Geometric scaling of correlation decay in chaotic billiards”, Phys. Rev. E, 51:5, part A (1995), R3807–R3810
Hakmi A., Bosco F., Antoniou I., “First return map of the periodic Lorentz gas”, Phys. Rev. E, 51:5 (1995), 3952–3956
Dorfman J.R., Gaspard P., “Chaotic scattering theory of transport and reaction-rate coefficients”, Phys. Rev. E, 51:1 (1995), 28–35
Hansen L.-U.W., Christensen M., Mosekilde E., “Deterministic analysis of the probability machine”, Phys. Scr., 51:1 (1995), 35–45
Simmel F., Eckert M., “Avoided crossings: Curvature distribution and behavior of eigenfunctions of pseudointegrable and chaotic billiards”, Phys. Rev. E, 51:6 (1995), 5435–5441
Gaspard P., Baras F., “Chaotic scattering and diffusion in the Lorentz gas”, Phys. Rev. E, 51:6 (1995), 5332–5352
Hackenbroich G., von Oppen F., “Periodic-orbit theory of quantum transport in antidot lattices”, Europhys. Lett., 29:2 (1995), 151–156
Gallavotti G., “Ergodicity, ensembles, irreversibility in Boltzmann and beyond”, J. Statist. Phys., 78:5-6 (1995), 1571–1589
Jonathan P. Bernick, Philip R. Baldwin, “Loss of channeling in a disordered lattice of focusing scatterers”, Physics Letters A, 197:4 (1995), 305
Wolfgang Bauer, David McGrew, Vladimir Zelevinsky, Peter Schuck, “Regular and chaotic dynamics in giant nuclear oscillations”, Nuclear Physics A, 583 (1995), 93
Per Dahlqvist, “Periodic orbit asymptotics for intermittent Hamiltonian systems”, Physica D: Nonlinear Phenomena, 83:1-3 (1995), 124
Barbara Dietz, Uzy Smilansky, “Scattering from a square obstacle”, Physica D: Nonlinear Phenomena, 86:1-2 (1995), 34
Dellago Ch., Posch H.A., Hoover W.G., “Lyapunov instability in a system of hard disks in equilibrium and nonequilibrium steady states”, Phys. Rev. E, 53:2 (1996), 1485–1501
Hansen K.T., Kohler A., “Chaotic scattering through potentials with rainbow singularities”, Phys. Rev. E, 54:6 (1996), 6214–6225
Bunimovich L., Casati G., Guarneri I., “Chaotic focusing billiards in higher dimensions”, Phys. Rev. Lett., 77:14 (1996), 2941–2944
Eaves L., Fromhold T.M., Sheard F.W., Wilkinson P.B., Henini M., Miura N., Takamasu T., “Quantum chaology in semiconductor heterostructures”, Phys. Scr., T68 (1996), 51–55
Bunimovich L.A., Spohn H., “Viscosity for a periodic two disk fluid: An existence proof”, Comm. Math. Phys., 176:3 (1996), 661–680
Krámli A., “Decay of correlations in one and two dimensions”, J. Statist. Phys., 83:1-2 (1996), 167–191
Dahlqvist P., “Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions”, J. Statist. Phys., 84:3-4 (1996), 773–795
Chernov N.I., Troubetzkoy S., “Measures with infinite Lyapunov exponents for the periodic Lorentz gas”, J. Statist. Phys., 83:1-2 (1996), 193–202
Artuso R., Casati G., Guarneri I., “Numerical experiments on billiards”, J. Statist. Phys., 83:1-2 (1996), 145–166
van Beijeren H., Dorfman J.R., Cohen E.G.D., Posch H.A., Dellago Ch., “Lyapunov exponents from kinetic theory for a dilute, field-driven Lorentz gas”, Phys. Rev. Lett., 77:10 (1996), 1974–1977
Simonazzi R., Tenenbaum A., “Anomalous fluctuations in low-temperature molecular dynamics simulations”, Phys. Rev. E, 54:1 (1996), 964–967
Tasnádi T., “The behavior of nearby trajectories in magnetic billiards”, J. Math. Phys., 37:11 (1996), 5577–5598
Vollmer J., Breymann W., Tél T., “Transient chaos: the origin of transport in driven systems”, Europhys. Lett., 35:9 (1996), 659–664
Lopes A., Markarian R., “Open billiards: invariant and conditionally invariant probabilities on Cantor sets”, SIAM J. Appl. Math., 56:2 (1996), 651–680
Chernov N.I., Haskell C., “Nonuniformly hyperbolic $K$-systems are Bernoulli”, Ergodic Theory Dynam. Systems, 16:1 (1996), 19–44
Chatterjee R., Jackson A.D., Balazs N.L., “Rigid-body motion, interacting billiards, and billiards on curved manifolds”, Phys. Rev. E, 53:6 (1996), 5670–5679
Fließer M., Schmidt G.J.O., Spohn H., “Magnetotransport of the Sinai billiard”, Phys. Rev. E, 53:6 (1996), 5690–5697
Zheng Zhigang, Hu Gang, Zhang Juyuan, “Ergodicity in hard-ball systems and Boltzmann's entropy”, Phys. Rev. E, 53:4 (1996), 3246–3252
McGrew D.A., Bauer W., “Constraint operator solution to quantum billiard problems”, Phys. Rev. E, 54:5 (1996), 5809–5818
Primack H., Schanz H., Smilansky U., Ussishkin I., “Penumbra diffraction in the quantization of dispersing billiards”, Phys. Rev. Lett., 76:10 (1996), 1615–1618
С. П. Новиков, Л. А. Бунимович, А. М. Вершик, Б. М. Гуревич, Е. И. Динабург, Г. А. Маргулис, В. И. Оселедец, С. А. Пирогов, К. М. Ханин, Н. Н. Ченцова, “Яков Григорьевич Синай (к шестидесятилетию со дня рождения)”, УМН, 51:4(310) (1996), 179–191 ; S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778
Elyutin P., Shan J., “Susceptibility of Chaotic Systems to Perturbations”, Phys. Rev. Lett., 77:25 (1996), 5043–5046
Raz T., Levine R.D., “Fast translational thermalization of extreme disequilibrium induced by cluster impact”, Chemical Physics, 213:1-3 (1996), 263–275
Zelevinsky V., Brown B.A., Frazier N., Horoi M., “The nuclear shell model as a testing ground for many-body quantum chaos”, Physics Reports, 276:2-3 (1996), 85–176
Per Dahlqvist, Roberto Artuso, “On the decay of correlations in Sinai billiards with infinite horizon”, Physics Letters A, 219:3-4 (1996), 212
Jian-zhong Gu, Xi-zhen Wu, Yi-zhong Zhuo, “The single-particle spectrum and its spacing and curvature distributions in rotating heavy nuclei”, Nuclear Physics A, 611:2-3 (1996), 315
J. Błocki, C. Jarzyński, W.J. Świa̧tecki, “Effect of dynamical correlations in a slowly pumped Knudsen gas”, Nuclear Physics A, 599:3-4 (1996), 486
Rupak Chatterjee, A.D. Jackson, “Surfing Arnold's web”, Nuclear Physics A, 606:1-2 (1996), 27
F. Simmel, M. Eckert, “Statistical measures for eigenfunctions of nonseparable quantum billiard systems”, Physica D: Nonlinear Phenomena, 97:4 (1996), 517
Ch. Dellago, H.A. Posch, “Lyapunov instability, local curvature, and the fluid-solid phase transition in two-dimensional particle systems”, Physica A: Statistical Mechanics and its Applications, 230:3-4 (1996), 364
S. Koga, “Global Scaling Laws in 3D Sinai's Billiards”, Progress of Theoretical Physics, 96:6 (1996), 1301
Taro Nagao, “Magnetotransport through Random Antidot Lattices”, J. Phys. Soc. Jpn, 65:8 (1996), 2606
Shinbrot T., Khakhar D.V., McCarthy J.J., Ottino J.M., “Role of voids in granular convection”, Phys. Rev. E, 55:5 (1997), 6121–6133
Lach-hab M., Blaisten-Barojas E., Sauer T., “Irregular scattering of particles confined to ring-bounded cavities”, J. Statist. Phys., 87:1-2 (1997), 137–146
Cheng Jian, “Surface billiards and nonvanishing Lyapunov exponents”, Acta Math. Sinica (N.S.), 13:1 (1997), 21–34
Taylor R.P., Newbury R., Sachrajda A.S., Feng Y., Coleridge P.T., Dettmann C., Zhu Ningjia, Guo Hong, Delage A., Kelly P.J., “Self-similar magnetoresistance of a semiconductor Sinai billiard”, Phys. Rev. Lett., 78:10 (1997), 1952–1955
Latz A., van Beijeren H., Dorfman J.R., “Lyapunov spectrum and the conjugate pairing rule for a thermostatted random Lorentz gas: kinetic theory”, Phys. Rev. Lett., 78:2 (1997), 207–210
Furukawa H., “Dynamics of phase separation of a simple fluid mixture: Comparison between molecular dynamics and numerical integration of the phenomenological equation”, Phys. Rev. E, 55:1 (1997), 1150–1161
Płoszajczak M., Srokowski T., “Solving the Langevin equation with stochastic algebraically correlated noise”, Phys. Rev. E, 55:5 (1997), 5126–5133
Taylor R.P., Micolich A.P., Newbury R., Dettmann C.P., Fromhold T.M., Semicond Sci Technol, 12:11 (1997), 1459–1464
Bäcker A., Schubert R., Stifter P., J Phys A Math Gen, 30:19 (1997), 6783–6795
Chernov N., “Entropy, Lyapunov exponents, and mean free path for billiards”, J. Statist. Phys., 88:1-2 (1997), 1–29
Matsuoka H., Martin R.F. (Jr.), “Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas”, J. Statist. Phys., 88:1-2 (1997), 81–103
Dahlqvist P., “The Lyapunov exponent in the Sinai billiard in the small scatterer limit”, Nonlinearity, 10:1 (1997), 159–173
Taylor R.P., Micolich A.P., Newbury R., “Correlation analysis of self-similarity in semiconductor billiards”, Phys. Rev. B, 56:20 (1997), R12733–R12736
Akishin P.G., Bosco F., Vinitsky S.I., “Helmholtz problem for plane periodical structures”, Computers & Mathematics with Applications, 34:5-6 (1997), 613–625
T.M. Fromhold, P.B. Wilkinson, L. Eaves, F.W. Sheard, P.C. Main, M. Henini, M.J. Carter, N. Miura, T. Takamasu, “Manifestations of quantum chaos in resonant tunnelling”, Chaos, Solitons & Fractals, 8:7-8 (1997), 1381
Katsuhiro Nakamura, “Introduction to chaos and quantum transport”, Chaos, Solitons & Fractals, 8:7-8 (1997), 971
Shiro Kawabata, Katsuhiro Nakamura, “Quantum chaotic transport in ballistic Aharonov-Bohm billiards”, Chaos, Solitons & Fractals, 8:7-8 (1997), 1085
P.V Elyutin, “Classical susceptibilities of chaotic systems”, Physics Letters A, 233:3 (1997), 175
R. Willox, I. Antoniou, J. Levitan, “Initial, non-exponential decay in billiards”, Physics Letters A, 226:3-4 (1997), 167
J.R. Dorfman, Henk van Beijeren, “Dynamical systems theory and transport coefficients: A survey with applications to Lorentz gases”, Physica A: Statistical Mechanics and its Applications, 240:1-2 (1997), 12
E.G.D. Cohen, “Dynamical ensembles in statistical mechanics”, Physica A: Statistical Mechanics and its Applications, 240:1-2 (1997), 43
Ch. Dellago, H.A. Posch, “Kolmogorov-Sinai entropy and Lyapunov spectra of a hard-sphere gas”, Physica A: Statistical Mechanics and its Applications, 240:1-2 (1997), 68
Artur Lopes, R.Daniel Mauldin, “Generic Properties of Open Billiards”, Journal of Mathematical Analysis and Applications, 205:1 (1997), 251
Yu.A. Kuperin, S.B. Levin, Yu.B. Melnikov, B.S. Pavlov, “Quantum Lorentz gas: Effective equations and spectral analysis”, Computers & Mathematics with Applications, 34:5-6 (1997), 599
S. Koga, “Scaling Laws of Moments in Sinai's Billiard Systems. I: The Case of Rectangular Lattice”, Progress of Theoretical Physics, 97:3 (1997), 363
Shiro Kawabata, Katsuhiro Nakamura, “Ballistic Conductance Fluctuation and Quantum Chaos in Sinai Billiard”, J. Phys. Soc. Jpn, 66:3 (1997), 712
A. Latz, “Lyapunov spectrum of a random Lorentz gas in a magnetic field”, Z. Phys. B, 103:3 (1997), 351
R. Willox, I. Antoniou, J. Levitan, “Decay of correlations and control of chaotic billiards”, Computers & Mathematics with Applications, 34:2-4 (1997), 391
Dana I., Feingold M., Wilkinson M., “Band distributions for quantum chaos on a torus”, Phys. Rev. Lett., 81:15 (1998), 3124–3127
Schweitzer F., Ebeling W., Tilch B., “Complex motion of Brownian particles with energy depots”, Phys. Rev. Lett., 80:23 (1998), 5044–5047
Micolich A.P., Taylor R.P., Bird J.P., Newbury R., Fromhold T.M., Cooper J., Aoyagi Y., Sugano T., “Scale factor mapping of statistical and exact self-similarity in billiards”, Semicond Sci. Technol., 13:8a (1998), A41–A43
Dorfman J.R., Latz A., van Beijeren H., “Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases”, Chaos and irreversibility (Budapest, 1997), Chaos, 8, no. 2, 1998, 444–454
Tasnádi T., “Hard chaos in magnetic billiards (on the hyperbolic plane)”, J. Math. Phys., 39:7 (1998), 3783–3804
Dullin H.R., “Linear stability in billiards with potential”, Nonlinearity, 11:1 (1998), 151–173
Daniels V.J., Vallières M., Yuan Jian Min, “Chaotic scattering on a billiard”, Phys. Rev. E, 57:2, part A (1998), 1519–1531
Bäcker A., Chernov N., “Generating partitions for two-dimensional hyperbolic maps”, Nonlinearity, 11:1 (1998), 79–87
Turaev D., Rom-Kedar V., “Elliptic islands appearing in near-ergodic flows”, Nonlinearity, 11:3 (1998), 575–600
Kawabata Sh., Nakamura K., “$h/2e$ oscillations and quantum chaos in ballistic Aharonov-Bohm billiards”, Phys. Rev. B, 57:11 (1998), 6282–6285
Wang Jian, Guo Hong, “Statistical analysis of magnetic-field spectra”, Phys. Rev. B, 58:19 (1998), 13094–13098
Alt H., Bäcker A., Dembowski C., Gräf H.-D., Hofferbert R., Rehfeld H., Richter A., “Mode fluctuation distribution for spectra of superconducting microwave billiards”, Phys. Rev. E, 58:2 (1998), 1737–1742
Bäcker A., Schubert R., Stifter P., “Rate of quantum ergodicity in Euclidean billiards”, Phys. Rev. E, 57:5, part A (1998), 5425–5447
Kawabata Sh., “Semiclassical theory of $h/e$ Aharonov-Bohm oscillation for doubly connected ballistic cavities”, Phys. Rev. B, 58:11 (1998), 6704–6707
Taylor R., Micolich A., Newbury R., Bird J., Fromhold T., Cooper J., Aoyagi Y., Sugano T., “Exact and statistical self-similarity in magnetoconductance fluctuations: a unified picture”, Phys. Rev. B, 58:17 (1998), 11107–11110
R.P Taylor, A.P Micolich, R Newbury, T.M Fromhold, C Dettmann, C.R Tench, “Experimental and theoretical investigations of clusters in the magneto-fingerprints of Sinai billiards”, Materials Science and Engineering: B, 51:1-3 (1998), 212
T.M. Fromhold, C.R. Tench, R.P. Taylor, A.P. Micolich, R. Newbury, “Self-similar conductance fluctuations in a Sinai billiard with a mixed chaotic phase space”, Physica B: Condensed Matter, 249-251 (1998), 334
Latchezar Stoyanov, “Instability and entropy for a class of dispersing billiards”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:6 (1998), 737
Gerland U., “Spectral statistics and dynamical localization: sharp transition in a generalized Sinai billiard”, Phys. Rev. Lett., 83:6 (1999), 1139–1142
Dittrich T., Koboldt G., Mehlig B., Schanz H., “Spectral statistics in chaotic systems with two identical, connected cells”, J. Phys. A, 32:39 (1999), 6791–6820
Robinett R.W., “Isolated versus nonisolated periodic orbits in variants of the two-dimensional square and circular billiards”, J. Math. Phys., 40:1 (1999), 101–122
Oloumi A., Teychenné D., “Controlling Hamiltonian chaos via Gaussian curvature”, Phys. Rev. E, 60:6 (1999), R6279–R6282
Harayama T., Shudo A., Tasaki Sh., “Semiclassical Fredholm determinant for strongly chaotic billiards”, Nonlinearity, 12:4 (1999), 1113–1149
Vered Rom-Kedar, Dmitry Turaev, “Big islands in dispersing billiard-like potentials”, Physica D: Nonlinear Phenomena, 130:3-4 (1999), 187
van Beijeren H., Latz A., Dorfman J.R., “Chaotic properties of dilute two- and three-dimensional random Lorentz gases. II. Open systems”, Phys. Rev. E, 63:1 (2000), 016312, 14 pp.
Kaplan L., Heller E.J., “Short-time effects on eigenstate structure in Sinai billiards and related systems”, Phys. Rev. E, 62:1, part A (2000), 409–426
Raychaudhuri S., Shapir Y., Chernyak V., Mukamel Sh., “Excitonic funneling in extended dendrimers with nonlinear and random potentials”, Phys. Rev. Lett., 85:2 (2000), 282–285
Loskutov A., Ryabov A.B., Akinshin L.G., J. Phys. A, 33:44 (2000), 7973–7986
Chu W. Kwang-Hua, “Preferred motions for many particles in confined slender domains”, Phys. Scr., 62:6 (2000), 453–457
Micolich A.P., Taylor R.P., Newbury R., Fromhold T.M., Tench C.R., “An investigation of Weierstrass self-similarity in a semiconductor billiard”, Europhys. Lett., 49:4 (2000), 417–423
Dellago Ch., Hoover Wm.G., “Finite-precision stationary states at and away from equilibrium”, Phys. Rev. E, 62:5 (2000), 6275–6281
Shinji Koga, “Numerical Evidence of Universal Scaling Laws of Moments in 2D Sinai's Billiard Systems”, J. Phys. Soc. Jpn, 69:7 (2000), 2011
Lopac V., “Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs”, Phys. Rev. E, 64:1 (2001), 016214, 8 pp.
Gaspard P., Claus I., Dorfman J.R., “Fractality of the hydrodynamic modes of diffusion”, Phys. Rev. Lett., 86:8 (2001), 1506–1509
Bandtlow O.F., Coveney P.V., “On the existence of dynamical systems with exponentially decaying collision operators”, J. Phys. A, 34:22 (2001), 4585–4599
Kokshenev V.B., Vicentini E., “From ballistic to Brownian motion through enhanced diffusion in vertex-splitting polygonal and disk-dispersing Sinai billiards”, Phys. Rev. E, 65:1 (2001), 015201, 4 pp.
Del Magno G., “Ergodicity of a class of truncated elliptical billiards”, Nonlinearity, 14:6 (2001), 1761–1786
С. В. Найденов, В. В. Яновский, “Геометро-динамический подход к бильярдным системам. I. Проективная инволюция бильярда. Прямая и обратная задачи”, ТМФ, 127:1 (2001), 110–124 ; S. V. Naydenov, V. V. Yanovskii, “Geometric-Dynamic Approach to Billiard Systems: I. Projective Involution of a Billiard, Direct and Inverse Problems”, Theoret. and Math. Phys., 127:1 (2001), 500–512
Г. А. Гальперин, “Биллиарды и упругие столкновения частиц и шаров”, Матем. просв., сер. 3, 5, МЦНМО, М., 2001, 65–99
Л. А. Бунимович, “Рассеяние, дефокусировка и астигматизм”, Матем. просв., сер. 3, 5, МЦНМО, М., 2001, 106–124
L. Kaplan, “Structure of quantum chaotic wave functions: ergodicity, localization, and transport”, Physica E: Low-dimensional Systems and Nanostructures, 9:3 (2001), 502
Bunimovich L.A., “Illumination problem and absolutely focusing mirrors”, Nonimaging Optics: Maximum Efficiency Light Transfer Vi, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 4446, 2001, 185–192
PIERRE GASPARD, “DYNAMICAL CHAOS AND NONEQUILIBRIUM STATISTICAL MECHANICS”, Int. J. Mod. Phys. B, 15:03 (2001), 209
Troy Shinbrot, F.J.. Muzzio, “Noise to order”, Nature, 410:6825 (2001), 251
Lopac V., Mrkonjić I., Radić D., “Chaotic dynamics and orbit stability in the parabolic oval billiard”, Phys. Rev. E, 66:3 (2002), 036202, 5 pp.
Dembowski C., Dietz B., Gräf H.-D., Heine A., Papenbrock T., Richter A., Richter C., “Experimental test of a trace formula for a chaotic three-dimensional microwave cavity”, Phys. Rev. Lett., 89:6 (2002), 064101, 4 pp.
Raychaudhuri S., Shapir Y., Mukamel Sh., “Disorder and funneling effects on exciton migration in treelike dendrimers”, Phys. Rev. E, 65:2 (2002), 021803, 12 pp.
Harayama T., Klages R., Gaspard P., “Deterministic diffusion in flower-shaped billiards”, Phys. Rev. E, 66:2 (2002), 026211, 7 pp.
Anishchenko V.S., Vadivasova T.E., Kopeikin A.S., Kurths J., Strelkova G.I., “Peculiarities of the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors in the presence of noise”, Phys. Rev. E, 65:3 (2002), 036206, 10 pp.
Foltin Ch., “Billiards with positive topological entropy”, Nonlinearity, 15:6 (2002), 2053–2076
С. В. Найденов, В. В. Яновский, “Инвариантные распределения в системах с упругими отражениями”, ТМФ, 130:2 (2002), 301–319 ; S. V. Naydenov, V. V. Yanovskii, “Invariant Distributions in Systems with Elastic Reflections”, Theoret. and Math. Phys., 130:2 (2002), 256–270
Kwang-Hua W. Chu, “Molecular flows in annuli with corrugated walls”, Eur. Phys. J. Appl. Phys., 17:2 (2002), 131–137
Pène F., “Averaging method for differential equations perturbed by dynamical systems”, ESAIM: P&S, 6 (2002), 33–88
L.N Gumen, J Arriaga, A.A Krokhin, “Manifestations of quantum chaos in spectra of 2D photonic crystals”, Physica E: Low-dimensional Systems and Nanostructures, 13:2-4 (2002), 459
С. В. Найденов, В. В. Яновский, А. В. Тур, “Биллиардная проблема в симметричных координатах”, Письма в ЖЭТФ, 75:8 (2002), 499–504 ; S. V. Naydenov, V. V. Yanovskii, A. V. Tur, “Problem of a billiard in symmetric coordinates”, JETP Letters, 75:8 (2002), 426–431
Kokshenev V.B., Vicentini E., “Slow relaxation in weakly open rational polygons”, Phys. Rev. E, 68:1 (2003), 016221, 8 pp.
Kwang-Hua Chu A., “Electrokinetic flows in a microdomain”, Phys. Rev. E, 67:4 (2003), 041106, 6 pp.
Vörös Z., Tasnádi T., Cserti J., Pollner P., “Tunable Lyapunov exponent in inverse magnetic billiards”, Phys. Rev. E, 67:6 (2003), 065202, 4 pp.
Lenci M., “Semidispersing billiards with an infinite cusp. II”, Chaos, 13:1 (2003), 105–111
Viscardy S., Gaspard P., “Viscosity in the escape-rate formalism”, Phys. Rev. E, 68:4 (2003), 041205, 10 pp.
В. В. Козлов, Д. В. Трещëв, “Эволюция мер в фазовом пространстве нелинейных гамильтоновых систем”, ТМФ, 136:3 (2003), 496–506 ; V. V. Kozlov, D. V. Treschev, “Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems”, Theoret. and Math. Phys., 136:3 (2003), 1325–1335
Л. Д. Пустыльников, “Обобщенные цепные дроби и эргодическая теория”, УМН, 58:1(349) (2003), 113–164 ; L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Russian Math. Surveys, 58:1 (2003), 109–159
Simányi N., “Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems”, Invent. Math., 154:1 (2003), 123–178
Deryabin M.V., Pustyl'nikov L.D., “Generalized relativistic billiards”, Regul. Chaotic Dyn., 8:3 (2003), 283–296
Deryabin M.V., Pustyl'nikov L.D., “On generalized relativistic billiards in external force fields”, Lett. Math. Phys., 63:3 (2003), 195–207
Nándor Bokor, Nir Davidson, “Chaotic and integrable reflective tube shapes for anamorphic, adiabatic transformation of diffuse light”, Optics Communications, 226:1-6 (2003), 89
Péter Bálint, I.P.éter Tóth, “Correlation Decay in Certain Soft Billiards”, Commun. Math. Phys, 243:1 (2003), 55
Mülken O., van Beijeren H., “Thermodynamic formalism for field-driven Lorentz gases”, Phys. Rev. E, 69:4 (2004), 046203, 9 pp.
Gaies A., El-Akrmi A., “Fractional variational principle in macroscopic picture”, Phys. Scr., 70:1 (2004), 7–10
Dembowski C., Dietz B., Friedrich T., Gräf H.-D., Heine A., Mejía-Monasterio C., Miski-Oglu M., Richter A., Seligman T.H., “First experimental evidence for quantum echoes in scattering systems”, Phys. Rev. Lett., 93:13 (2004), 134102, 4 pp.
Simanyi N., “Proving the ergodic hypothesis for billiards with disjoint cylindric scatterers”, Nonlinearity, 17:1 (2004), 1–21
Deryabin M.V., Pustyl'nikov L.D., “Exponential attractors in generalized relativistic billiards”, Comm. Math. Phys., 248:3 (2004), 527–552
P BALINT, “Mixing and its rate in ?soft? and ?hard? billiards motivated by the Lorentz process”, Physica D: Nonlinear Phenomena, 187:1-4 (2004), 128
I Claus, “Fractals and dynamical chaos in a random 2D Lorentz gas with sinks”, Physica D: Nonlinear Phenomena, 187:1-4 (2004), 146
Shinbrot T., “Fluid dynamics: Drat such custard!”, Appl. Opt., 438:7070 (2005), 922–923
Jenkinson O., “Maximum hitting frequency and fastest mean return time”, Nonlinearity, 18:5 (2005), 2305–2321
Bunimovich L.A., Demers M.F., “Deterministic Models of the Simplest Chemical Reactions”, J. Stat. Phys., 120:1-2 (2005), 239–252
Vesely F.J., “Explaining Gibbsean phase space to second year students”, Eur. J. Phys., 26:2 (2005), 243–250
Evesque P., Palencia F., Lecoutre-Chabot C., Beysens D., Garrabos Y., “Granular gas in weightlessness: The limit case of very low densities of non interacting spheres”, Microgravity Sci. Technol., 16:1-4 (2005), 280–284
Goussev A., Dorfman J.R., “Lyapunov spreading of semiclassical wave packets for the Lorentz gas: Theory and applications”, Phys. Rev. E, 71:2 (2005), 026225, 10 pp.
van Beijeren H., Mülken O., “Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions”, Phys. Rev. E, 71:3 (2005), 036213, 7 pp.
Schanz H., Prusty M., “Directed chaos in a billiard chain with transversal magnetic field”, J. Phys. A, 38:47 (2005), 10085–10100
Chernov N., Zhang H.-K., “Billiards with polynomial mixing rates”, Nonlinearity, 18:4 (2005), 1527–1553
Castaldi G., Fiumara V., Galdi V., Pierro V., Pinto I.M., Felsen L.B., “Ray-chaotic footprints in deterministic wave dynamics: a test model with coupled Floquet-type and ducted-type mode characteristics”, IEEE Trans. Antennas Propagat., 53:2 (2005), 753–765
В. С. Анищенко, Т. Е. Вадивасова, Г. А. Окрокверцхов, Г. И. Стрелкова, “Статистические свойства динамического хаоса”, УФН, 175:2 (2005), 163–179 ; V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, G. I. Strelkova, “Statistical properties of dynamical chaos”, Phys. Usp., 48:2 (2005), 151–166
Valery Kokshenev, “On Chaotic Dynamics in Rational Polygonal Billiards”, SIGMA, 1 (2005), 014, 9 pp.
Otto E. Rossler,, Ramis Movassagh, “Bitemporal Dynamic Sinai Divergence: An Energetic Analog to Boltzmann's Entropy?”, International Journal of Nonlinear Sciences and Numerical Simulation, 6:4 (2005), 349
N. CHERNOV, H.-K. ZHANG, “A FAMILY OF CHAOTIC BILLIARDS WITH VARIABLE MIXING RATES”, Stoch. Dyn, 05:04 (2005), 535
Hurtado P.I., Redner S., “Simplest piston problem. I. Elastic collisions”, Phys. Rev. E, 73:1 (2006), 016136, 8 pp.
Radionov S., “Classical chaos effect on nuclear collective motion”, Phys. Scr., t125 (2006), 151–157
Kruis H.V., Panja D., van Beijeren H., “Systematic density expansion of the Lyapunov exponents for a two-dimensional random Lorentz gas”, J. Stat. Phys., 124:2-4 (2006), 823–842
Boca F.P., Zaharescu A., “The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit”, Comm. Math. Phys., 269:2 (2006), 425–471
Dietz B., Friedrich T., Miski-Oglu M., Richter A., Seligman T.H., Zapfe K., “Nonperiodic echoes from mushroom billiard hats”, Phys. Rev. E, 74:5 (2006), 056207, 8 pp.
Chernov N., “Advanced statistical properties of dispersing billiards”, J. Stat. Phys., 122:6 (2006), 1061–1094
Rapoport A., Rom-Kedar V., “Nonergodicity of the motion in three-dimensional steep repelling dispersing potentials”, Chaos, 16:4 (2006), 043108, 6 pp.
Lansel S., Porter M.A., Bunimovich L.A., “One-particle and few-particle billiards”, Chaos, 16:1 (2006), 013129, 12 pp.
Hongqiang Xia, “Distribution of closed orbits of billiard flows on the plane”, Nonlinear Analysis: Theory, Methods & Applications, 64:6 (2006), 1262
Valery B. Kokshenev, Eduardo Vicentini, “Physical insight into superdiffusive dynamics of Sinai billiard through collision statistics”, Physica A: Statistical Mechanics and its Applications, 360:2 (2006), 197
Zorich A., “Flat surfaces”, Frontiers in Number Theory, Physics and Geometry I - ON RANDOM MATRICES, ZETA FUNCTIONS, AND DYNAMICAL SYSTEMS, 2006, 439–585
DANIEL K. WÓJCIK, “QUANTUM MAPS WITH SPACE EXTENT: A PARADIGM FOR LATTICE QUANTUM WALKS”, Int. J. Mod. Phys. B, 20:14 (2006), 1969
Leonel E.D., “Corrugated waveguide under scaling investigation”, Phys. Rev. Lett., 98:11 (2007), 114102, 4 pp.
Deryabin M.V., Pustyl'nikov L.D., “Nonequilibrium gas and generalized billiards”, J. Stat. Phys., 126:1 (2007), 117–132
Chernov N., Markarian R., “Dispersing billiards with cusps: slow decay of correlations”, Comm. Math. Phys., 270:3 (2007), 727–758
Rapoport A., Rom-Kedar V., Turaev D., “Approximating Multi-Dimensional Hamiltonian Flows by Billiards”, Comm. Math. Phys., 272:3 (2007), 567–600
Dietz B., Friedrich T., Miski-Oglu M., Richter A., Schäfer F., “Spectral properties of Bunimovich mushroom billiards”, Phys. Rev. E, 75:3 (2007), 035203, 4 pp.
Chernov N., “A stretched exponential bound on time correlations for billiard flows”, J. Stat. Phys., 127:1 (2007), 21–50
Eckmann J.-P., Jacquet Ph., “Controllability for chains of dynamical scatterers”, Nonlinearity, 20:7 (2007), 1601–1617
Chernov N., Dolgopyat D., “Diffusive motion and recurrence on an idealized Galton board”, Phys. Rev. Lett., 99:3 (2007), 030601, 4 pp.
Karlis A.K., Papachristou P.K., Diakonos F.K., Constantoudis V., Schmelcher P., “Fermi acceleration in the randomized driven Lorentz gas and the Fermi-Ulam model”, Phys. Rev. E, 76:1 (2007), 016214, 17 pp.
Kobre E., Young Lai-Sang, “Extended systems with deterministic local dynamics and random jumps”, Comm. Math. Phys., 275:3 (2007), 709–720
Kamphorst S.O., Leonel E.D., da Silva J.K.L., “The presence and lack of Fermi acceleration in nonintegrable billiards”, J. Phys. A, 40:37 (2007), F887–F893
А. Ю. Лоскутов, “Динамический хаос. Системы классической механики”, УФН, 177:9 (2007), 989–1015 ; A. Yu. Loskutov, “Dynamical chaos: systems of classical mechanics”, Phys. Usp., 50:9 (2007), 939–964
Jürgen F. Stilck, “Particle–wall collision statistics in the open circular billiard”, Physica A: Statistical Mechanics and its Applications, 381 (2007), 22
Gérard G. Emch, “Models and the dynamics of theory-building in physics. Part II—Case studies”, Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 38:4 (2007), 683
Hongqiang Xia, Yunfei Ge, Zhengjie Zhang, “Equidistribution of closed orbits of billiard flows on the plane”, Acta Mathematica Scientia, 27:3 (2007), 465
Chernov N., Zhang H.-K., “Regularity of Bunimovich's stadia”, Regular & Chaotic Dynamics, 12:3 (2007), 335–356
Melbourne I., “Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows”, Trans. Am. Math. Soc., 359:5 (2007), 2421–2441
N. Chernov, H. -K. Zhang, “Improved Estimates for Correlations in Billiards”, Commun. Math. Phys, 277:2 (2007), 305
Bardos C., Garnier J., Papanicolaou G., “Identification of Green's functions singularities by cross correlation of noisy signals”, Inverse Problems, 24:1 (2008), 015011, 26 pp.
Rapoport A., Rom-Kedar V., “Chaotic scattering by steep repelling potentials”, Phys. Rev. E, 77:1 (2008), 016207, 16 pp.
Rapoport A., Rom-Kedar V., Turaev D., “Stability in high dimensional steep repelling potentials”, Comm. Math. Phys., 279:2 (2008), 497–534
Courbage M., Edelman M., Saberi Fathi S.M., Zaslavsky G.M., “Problem of transport in billiards with infinite horizon”, Phys. Rev. E, 77:3 (2008), 036203, 5 pp.
Malinin S.V., Chernyak V.Y., “Classical nonlinear response of a chaotic system. I. Collective resonances”, Phys. Rev. E, 77:5 (2008), 056201, 21 pp.
Gelfreich V., Turaev D., “Unbounded energy growth in Hamiltonian systems with a slowly varying parameter”, Comm. Math. Phys., 283:3 (2008), 769–794
Gendelman O.V., Manevitch L.I., “Discrete breathers in vibroimpact chains: analytic solutions”, Phys. Rev. E, 78:2 (2008), 026609, 6 pp.
Bachurin P., Bálint P., Tóth I.P., “Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards”, Israel J. Math., 167:1 (2008), 155–175
Bunimovich L.A., Del Magno G., “Semi-focusing billiards: ergodicity”, Ergodic Theory Dynam. Systems, 28:5 (2008), 1377–1417
Malinin S.V., Chernyak V.Y., “Collective oscillations in the classical nonlinear response of a chaotic system”, Phys. Rev. E, 77:2 (2008), 025201, 4 pp.
Taylor M.P., Isik K., Luettmer-Strathmann J., “Dynamics of a single polymer chain: ergodicity and conformation of a rotating chain”, Phys. Rev. E, 78:5 (2008), 051805, 13 pp.
Dietz B., Mößner B., Papenbrock T., Reif U., Richter A., “Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard”, Phys. Rev. E, 77:4 (2008), 046221, 10 pp.
Castaldi G., Galdi V., Pinto I.M., “A study of ray-chaotic cylindrical scatterers”, IEEE Trans. Antennas Propagat., 56:8 (2008), 2638–2648
L BUSSOLARI, M LENCI, “Hyperbolic billiards with nearly flat focusing boundaries, I”, Physica D: Nonlinear Phenomena, 237:18 (2008), 2272
Domokos Szász, “Some challenges in the theory of (semi)-dispersing billiards”, Nonlinearity, 21:10 (2008), T187
Denis Gouvêa Ladeira, Jafferson Kamphorst Leal da Silva, “Scaling features of a breathing circular billiard”, J. Phys. A: Math. Theor, 41:36 (2008), 365101
F.M. Zanetti, E. Vicentini, M.G.E. da Luz, “Eigenstates and scattering solutions for billiard problems: A boundary wall approach”, Annals of Physics, 323:7 (2008), 1644
Balint P., Melbourne I., “Decay of Correlations and Invariance Principles for Dispersing Billiards with Cusps, and Related Planar Billiard Flows”, J Stat Phys, 133:3 (2008), 435–447
Chernov N., “Sinai billiards under small external forces II”, Ann Henri Poincaré, 9:1 (2008), 91–107
Chernov N., Zhang H.-K., “Improved estimates for correlations in billiards”, Comm Math Phys, 277:2 (2008), 305–321
QIUDONG WANG, ALI OKSASOGLU, “RANK ONE CHAOS: THEORY AND APPLICATIONS”, Int. J. Bifurcation Chaos, 18:05 (2008), 1261
Dolgopyat D. Szasz D. Varju T., “Recurrence Properties of Planar Lorentz Process”, Duke Math. J., 142:2 (2008), 241–281
M. Courbage, S.M. Saberi Fathi, “Computation of entropy increase for Lorentz gas and hard disks”, Communications in Nonlinear Science and Numerical Simulation, 13:2 (2008), 444
Simányi N., “Conditional proof of the Boltzmann-Sinai ergodic hypothesis”, Invent. Math., 177:2 (2009), 381–413
Oliveira D.F.M., Bizão R.A., Leonel E.D., “Scaling properties of a hybrid Fermi-Ulam-bouncer model”, Math. Probl. Eng., 2009, 213857, 13 pp.
Arroyo A., Markarian R., Sanders D.P., “Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries”, Nonlinearity, 22:7 (2009), 1499–1522
Simula T., Stenlund M., “Deterministic walks in quenched random environments of chaotic maps”, J. Phys. A, 42:24 (2009), 245101, 14 pp.
Д. И. Долгопят, Н. И. Чернов, “Аномальный ток в периодических газах Лоренца с бесконечным горизонтом”, УМН, 64:4(388) (2009), 73–124 ; D. I. Dolgopyat, N. I. Chernov, “Anomalous current in periodic Lorentz gases with infinite horizon”, Russian Math. Surveys, 64:4 (2009), 651–699
Chernov N., Zhang Hong-Kun, “On statistical properties of hyperbolic systems with singularities”, J. Stat. Phys., 136:4 (2009), 615–642
Ю. Е. Кузовлев, “Молекулярное случайное блуждание и группа инвариантности уравнения Боголюбова”, ТМФ, 160:3 (2009), 517–533 ; Yu. E. Kuzovlev, “Molecular random walk and a symmetry group of the Bogoliubov equation”, Theoret. and Math. Phys., 160:3 (2009), 1301–1315
Pène F., “Transient random walk in $\mathbb Z^2$ with stationary orientations”, ESAIM Probab. Stat., 13 (2009), 417–436
Petkov V., Stoyanov L., “Correlations for pairs of periodic trajectories for open billiards”, Nonlinearity, 22:11 (2009), 2657–2679
Leonel E.D., “Phase transition in dynamical systems: defining classes of universality for two-dimensional Hamiltonian mappings via critical exponents”, Math. Probl. Eng., 2009, 367921, 22 pp.
Markarian R., Pujals E.J., Sambarino M., “Pinball billiards with dominated splitting”, Ergod. Th. Dynam. Sys., 2009
Bäcker A., Dietz B., Friedrich T., Miski-Oglu M., Richter A., Schäfer F., Tomsovic S., “Friedel oscillations in microwave billiards”, Phys. Rev. E, 80:6 (2009), 066210, 5 pp.
Chernov N., Dolgopyat D., Brownian Brownian motion. I, Mem. Amer. Math. Soc., 198, no. 927, 2009, viii+193 pp.
Dettmann C.P., Georgiou O., “Survival probability for the stadium billiard”, Physica D: Nonlinear Phenomena, 238:23-24 (2009), 2395–2403
Bunimovich L.A., “Criterion of absolute focusing for focusing component of billiards”, Regular & Chaotic Dynamics, 14:1 (2009), 42–48
J. Acacio de Barros, Patrick Suppes, “Quantum mechanics, interference, and the brain”, Journal of Mathematical Psychology, 53:5 (2009), 306
Chernov N., Dolgopyat D., “The Calton Board: Limit Theorems and Recurrence”, J Amer Math Soc, 22:3 (2009), 821–858
Dolgopyat D., Szasz D., Varju T., “Limit Theorems for Locally Perturbed Planar Lorentz Processes”, Duke Math J, 148:3 (2009), 459–499
Melbourne I. Nicol M., “A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems”, Ann. Probab., 37:2 (2009), 478–505
Melbourne I., “Decay of Correlations for Slowly Mixing Flows”, Proc. London Math. Soc., 98 (2009), 163–190
Pène F., Saussol B., “Back to balls in billiards”, Comm. Math. Phys., 293:3 (2010), 837–866
Ryabov A.B., Loskutov A., “Time-dependent focusing billiards and macroscopic realization of Maxwell's demon”, J. Phys. A, 43:12 (2010), 125104, 15 pp.
С. В. Болотин, Д. В. Трещëв, “Формула Хилла”, УМН, 65:2(392) (2010), 3–70 ; S. V. Bolotin, D. V. Treschev, “Hill's formula”, Russian Math. Surveys, 65:2 (2010), 191–257
Lenci M., “On infinite-volume mixing”, Comm. Math. Phys., 298:2 (2010), 485–514
Koiller J., Young Lai-Sang, “Coupled map networks”, Nonlinearity, 23:5 (2010), 1121–1141
Stenlund M., “A strong pair correlation bound implies the CLT for Sinai billiards”, J. Statist. Phys., 140:1 (2010), 154–169
Chernov N., Dolgopyat D., “Lorentz gas with thermostatted walls”, Ann. Henri Poincaré, 11:6 (2010), 1117–1169
Hackenbroich G., von Oppen F., “Quantum corrections to the conductivity and periodic orbits: Integrable systems”, Ann. Physics, 508:8 (2010), 696–709
Anteneodo C., Vallejos R.O., “Lyapunov exponent of the random frequency oscillator: cumulant expansion approach”, J. Phys. Conf. Ser., 246 (2010), 012002, 9 pp.
Feres R., Zhang Hong-Kun, “The spectrum of the billiard Laplacian of a family of random billiards”, J. Statist. Phys., 141:6 (2010), 1039–1054
Petkov V., Stoyanov L., “Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function”, APDE, 3:4 (2010), 427–489
Kwang-Hua, Chu Zotin, “Dispersion relations of plane waves in system of hard-disk-like rotating gases”, Eur. Phys. J. Appl. Phys., 52:3 (2010), 31304
Tudorovskiy T., Kuhl U., Stöckmann H.-J., “Singular statistics revised”, New J. Phys., 12:12 (2010), 123021, 28 pp.
А. Ю. Лоскутов, “Очарование хаоса”, УФН, 180:12 (2010), 1305–1329 ; A. Yu. Loskutov, “Fascination of chaos”, Phys. Usp., 53:12 (2010), 1257–1280
Bernard E.P., Chanal C., Krauth W., “Damage spreading and coupling in Markov chains”, Europhys Lett EPL, 92:6 (2010), 60004
Chernov N., “The work of Dmitry Dolgopyat on physical models with moving particles”, Journal of Modern Dynamics, 4:2 (2010), 243–255
Oliveira D.F.M., Leonel E.D., “On the dynamical properties of an elliptical–oval billiard with static boundary”, Communications in Nonlinear Science and Numerical Simulation, 15:4 (2010), 1092–1102
А. Ю. Лоскутов, А. Б. Рябов, А. К. Краснова, О. А. Чичигина, “Бильярды с возмущаемыми границами и некоторые их свойства”, Нелинейная динам., 6:3 (2010), 573–604
J.F. Laprise, A. Hosseinizadeh, J. Lamy-Poirier, R. Zomorrodi, J. Kröger, H. Kröger, “Universality in level spacing fluctuations of a chaotic optical billiard”, Physics Letters A, 374:19-20 (2010), 2000
Alexander Loskutov, Alexei Ryabov, Edson D. Leonel, “Separation of particles in time-dependent focusing billiards”, Physica A: Statistical Mechanics and its Applications, 389:23 (2010), 5408
Diego F.M. Oliveira, Edson D. Leonel, “Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions”, Physica A: Statistical Mechanics and its Applications, 389:5 (2010), 1009
Yi-Chiuan Chen, “On topological entropy of billiard tables with small inner scatterers”, Advances in Mathematics, 224:2 (2010), 432
C. Bianca, “On the mathematical transport theory in microporous media: The billiard approach”, Nonlinear Analysis: Hybrid Systems, 4:4 (2010), 699
Sinai Y.G., “Chaos Theory Yesterday, Today and Tomorrow”, J Stat Phys, 138:1–3 (2010), 2–7
Demers M., Wright P., Young L.-S., “Escape Rates and Physically Relevant Measures for Billiards with Small Holes”, Comm Math Phys, 294:2 (2010), 353–388
Bunimovich L.A., Grigo A., “Focusing Components in Typical Chaotic Billiards Should be Absolutely Focusing”, Comm Math Phys, 293:1 (2010), 127–143
Liverani C., “On the Work and Vision of Dmitry Dolgopyat”, J. Mod. Dyn., 4:2 (2010), 211–225
Hong-Kun Zhang, “MIXING RATE FOR RECTANGULAR BILLIARDS WITH DIAMOND RECTANGLES”, American Journal of Mathematical and Management Sciences, 30:1-2 (2010), 53
Harayama T., Shinohara S., “Two-dimensional microcavity lasers”, Laser & Photon. Rev., 5:2 (2011), 247–271
Gelfreich V., Rom-Kedar V., Shah K., Turaev D., “Robust exponential acceleration in time-dependent billiards”, Phys. Rev. Lett., 106:7 (2011), 074101, 4 pp.
Gilbert Th., Sanders D.P., “Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape”, New J. Phys, 13:2 (2011), 023040, 50 pp.
Novikov D.S., Fieremans E., Jensen J.H., Helpern J.A., “Random walks with barriers”, Nat. Phys., 2011
Stoyanov L., “Non-integrability of open billiard flows and Dolgopyat-type estimates”, Ergod. Th. Dynam. Sys., 2011
Livorati A.L.P., Loskutov A., Leonel E.D., “A family of stadium-like billiards with parabolic boundaries under scaling analysis”, J. Phys. A, 44:17 (2011), 175102, 12 pp.
Shah K., “Energy growth rate in smoothly oscillating billiards”, Phys. Rev. E, 83:4 (2011), 046215, 4 pp.
Hong-Kun Zhang, “Estimates for correlations in billiards with large arcs”, Acta Math. Appl. Sin. Engl. Ser, 27:3 (2011), 381
Juliano A. de Oliveira, Edson D. Leonel, “Locating invariant tori in a family of two-dimensional Hamiltonian mappings”, Physica A: Statistical Mechanics and its Applications, 2011
Astrid S de Wijn, Henk van Beijeren, “A radius of curvature approach to the Kolmogorov–Sinai entropy of dilute hard particles in equilibrium”, J. Stat. Mech, 2011:08 (2011), P08012
E. M. Ganapolskii, Yu. V. Tarasov, L. D. Shostenko, “Spectral properties of cylindrical quasioptical cavity resonator with random inhomogeneous side boundary”, Phys. Rev. E, 84:2 (2011)
P. Bálint, N. Chernov, D. Dolgopyat, “Limit Theorems for Dispersing Billiards with Cusps”, Commun. Math. Phys, 2011
A. ARBIETO, R. MARKARIAN, M. J. PACIFICO, R. SOARES, “Scaling rate for semi-dispersing billiards with non-compact cusps”, Ergod. Th. Dynam. Sys, 2011, 1
Е. А. Гуткин, “Динамика биллиардa: обзорная статья с акцентом на нерешенные задачи”, Нелинейная динам., 7:3 (2011), 489–512
Carl P. Dettmann, “New Horizons in Multidimensional Diffusion: The Lorentz Gas and the Riemann Hypothesis”, J Stat Phys, 2011
Alexander Jonathan Vidgop, Itzhak Fouxon, “Evolution of collision numbers for a chaotic gas dynamics”, Phys. Rev. E, 84:5 (2011)
Edson D. Leonel, Diogo R. da Costa, Carl P. Dettmann, “Scaling invariance for the escape of particles from a periodically corrugated waveguide”, Physics Letters A, 2011
M. Leitner, M.P. Leubner, Z. Vörös, “Creating kappa-like distributions from a Galton board”, Physica A: Statistical Mechanics and its Applications, 390:7 (2011), 1248
V. Lopac, A. Šimić, “Chaotic properties of the truncated elliptical billiards”, Communications in Nonlinear Science and Numerical Simulation, 16:1 (2011), 309
Carlo Bianca, “Weyl-flow and the conformally symplectic structure of thermostatted billiards: The problem of the hyperbolicity”, Nonlinear Analysis: Hybrid Systems, 5:1 (2011), 32
IVÁN F. HERRERA-GONZÁLEZ, GABRIEL ARROYO-CORREA, ALBERTO MENDOZA-SUÁREZ, EDUARDO S. TUTUTI, “STUDY OF THE RESISTIVITY IN A CHANNEL WITH DEPHASED RIPPLES”, Int. J. Mod. Phys. B, 25:05 (2011), 683
I. MIKOSS, P. GARCÍA, “AN EXACT MAP FOR A CHAOTIC BILLIARD”, Int. J. Mod. Phys. B, 25:05 (2011), 673
Steffen Löck, Arnd Bäcker, Roland Ketzmerick, “Coupling of bouncing-ball modes to the chaotic sea and their counting function”, Phys. Rev. E, 85:1 (2012)
Keith Burns, Howard Masur, Amie Wilkinson, “The Weil-Petersson geodesic flow is ergodic”, Ann. Math, 175:2 (2012), 835
Raúl Vallejos, Celia Anteneodo, “Generalized Lyapunov exponents of the random harmonic oscillator: Cumulant expansion approach”, Phys. Rev. E, 85:2 (2012)
Edson D. Leonel, Carl P. Dettmann, “Recurrence of particles in static and time varying oval billiards”, Physics Letters A, 2012
André L.P. Livorati, Alexander Loskutov, Edson D. Leonel, “A peculiar Maxwell’s Demon observed in a time-dependent stadium-like billiard”, Physica A: Statistical Mechanics and its Applications, 2012
A.P. Micolich, A.M. See, B.C. Scannell, C.A. Marlow, T.P. Martin, I. Pilgrim, A.R. Hamilton, H. Linke, R.P. Taylor, “Is it the boundaries or disorder that dominates electron transport in semiconductor ‘billiards’?”, Fortschr. Phys, 2012, n/a
André L. P. Livorati, Ibere^ L. Caldas, Edson D. Leonel, “Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard”, Chaos, 22:2 (2012), 026122
N. Chernov, A. Korepanov, N. Simányi, “Stable regimes for hard disks in a channel with twisting walls”, Chaos, 22:2 (2012), 026105
V. Rom-Kedar, D. Turaev, “Billiards: A singular perturbation limit of smooth Hamiltonian flows”, Chaos, 22:2 (2012), 026102
Diego F. M. Oliveira, Edson D. Leonel, “In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas”, Chaos, 22:2 (2012), 026123
GIANLUIGI DEL MAGNO, ROBERTO MARKARIAN, “A local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularities”, Ergod. Th. Dynam. Sys, 2012, 1
V. Gelfreich, V. Rom-Kedar, D. Turaev, “Fermi acceleration and adiabatic invariants for non-autonomous billiards”, Chaos, 22:3 (2012), 033116
Hong-Kun Zhang, “Free path of billiards with flat points”, DCDS-A, 32:12 (2012), 4445
Stefano Bernardi, J. S. Hansen, Federico Frascoli, B. D. Todd, Carl P. Dettmann, “Ergodicity of a Single Particle Confined in a Nanopore”, J Stat Phys, 2012
A. Karlis, F. Diakonos, C. Petri, P. Schmelcher, “Criticality and Strong Intermittency in the Lorentz Channel”, Phys. Rev. Lett, 109:11 (2012)
DIEGO F. M. OLIVEIRA, MARKO ROBNIK, “SCALING INVARIANCE IN A TIME-DEPENDENT ELLIPTICAL BILLIARD”, Int. J. Bifurcation Chaos, 22:09 (2012), 1250207
Giulio Casati, Tomaž Prosen, “Time Irreversible Billiards with Piecewise-Straight Trajectories”, Phys. Rev. Lett, 109:17 (2012)
А. А. Макаров, А. Л. Малиновский, Е. А. Рябов, “Внутримолекулярное перераспределение колебательной энергии: от спектров высокого разрешения к динамике в реальном времени”, УФН, 182:10 (2012), 1047–1080 ; A. A. Makarov, A. L. Malinovsky, E. A. Ryabov, “Intramolecular vibrational redistribution: from high-resolution spectra to real-time dynamics”, Phys. Usp., 55:10 (2012), 977–1007
J. Armstrong, S. Åberg, S. Reimann, V. Zelevinsky, “Complexity of quantum states in the two-dimensional pairing model”, Phys. Rev. E, 86:6 (2012)
Feres R., Zhang H.-K., “Spectral Gap for a Class of Random Billiards”, Commun. Math. Phys., 313:2 (2012), 479–515
Беккер В.Ф., “Динамика механического взаимодействия элементов подвижной шаровой насадки”, Научно-технический вестник поволжья, 2012, № 2, 94–98
E.D.. Leonel, M.W.. Beims, L.A.. Bunimovich, “Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems”, Chaos, 22:2 (2012), 026101
R Markarian, M J Pacifico, J L Vieitez, “Exponential speed of mixing for skew-products with singularities”, Nonlinearity, 26:1 (2013), 269
Rui Yang, Liang Huang, Ying-Cheng Lai, Celso Grebogi, Louis M. Pecora, “Harnessing quantum transport by transient chaos”, Chaos, 23:1 (2013), 013125
Massimo Tessarotto, Claudio Cremaschini, Marco Tessarotto, “On the conditions of validity of the Boltzmann equation and Boltzmann H-theorem”, Eur. Phys. J. Plus, 128:3 (2013)
D. M. Naplekov, A. V. Tur, V. V. Yanovsky, “Scattering by a boundary with complex structure”, Phys. Rev. E, 87:4 (2013)
Lai-Sang Young, “Mathematical theory of Lyapunov exponents”, J. Phys. A: Math. Theor, 46:25 (2013), 254001
Nándor Simányi, “Singularities and non-hyperbolic manifolds do not coincide”, Nonlinearity, 26:6 (2013), 1703
G. Benettin, “Ergodicity and Time-Scales for Statistical Equilibrium in Classical Dynamical Systems”, Progress of Theoretical Physics Supplement, 116 (2013), 207
Giacomo Gradenigo, Alessandro Sarracino, Andrea Puglisi, Hugo Touchette, “Fluctuation relations without uniform large deviations”, J. Phys. A: Math. Theor, 46:33 (2013), 335002
S.C. Kapfer, Werner Krauth, “Sampling from a polytope and hard-disk Monte Carlo”, J. Phys.: Conf. Ser, 454 (2013), 012031
Mikko Stenlund, Lai-Sang Young, Hongkun Zhang, “Dispersing Billiards with Moving Scatterers”, Commun. Math. Phys, 2013
D.F..M. Oliveira, Thorsten Pöschel, “Competition between unlimited and limited energy growth in a two-dimensional time-dependent billiard”, Physics Letters A, 2013
Sebastian Schröter, Paul-Antoine Hervieux, Giovanni Manfredi, Johannes Eiglsperger, Javier Madroñero, “Exact treatment of planar two-electron quantum dots: Effects of anharmonicity on the complexity”, Phys. Rev. B, 87:15 (2013)
M.F.. Demers, Hong-Kun Zhang, “A Functional Analytic Approach to Perturbations of the Lorentz Gas”, Commun. Math. Phys, 2013
Nikolai Chernov, Hong-Kun Zhang, Pengfei Zhang, “Electrical Current in Sinai Billiards Under General Small Forces”, J Stat Phys, 2013
D. S. Grebenkov, B.-T. Nguyen, “Geometrical Structure of Laplacian Eigenfunctions”, SIAM Rev, 55:4 (2013), 601
Л. Д. Пустыльников, М. В. Дерябин, “Чëрные дыры и обобщëнные релятивистские биллиарды”, Препринты ИПМ им. М. В. Келдыша, 2013, 054, 36 с.
Jingyu Chen, Luke Mohr, Hong-Kun Zhang, Pengfei Zhang, “Ergodicity of the generalized lemon billiards”, Chaos, 23:4 (2013), 043137
М. Н. Давлетшин, “Формула Хилла для $g$-периодических траекторий лагранжевых систем”, Тр. ММО, 74, № 1, МЦНМО, М., 2013, 75–113 ; M. N. Davletshin, “Hill’s formula for $g$-periodic trajectories of Lagrangian systems”, Trans. Moscow Math. Soc., 74 (2013), 65–96
Young L.-S., “Understanding Chaotic Dynamical Systems”, Commun. Pure Appl. Math., 66:9 (2013), 1439–1463
Gianluigi Del Magno, Roberto Markarian, “Singular Sets of Planar Hyperbolic Billiards are Regular”, Regul. Chaotic Dyn., 18:4 (2013), 425–452
Wright P., “Estimates of Hausdorff Dimension for Non-Wandering Sets of Higher Dimensional Open Billiards”, Can. J. Math.-J. Can. Math., 65:6 (2013), 1384–1400
L. D. Pustyl'nikov, M. V. Deryabin, “Nonequilibrium gas, entropy and generalized billiards”, Препринты ИПМ им. М. В. Келдыша, 2014, 003, 10 с.
Elena Gryazina, Boris Polyak, “Random sampling: Billiard Walk algorithm”, European Journal of Operational Research, 2014
D. S. Novikov, J. H. Jensen, J. A. Helpern, E. Fieremans, “Revealing mesoscopic structural universality with diffusion”, Proceedings of the National Academy of Sciences, 111:14 (2014), 5088
Massimo Tessarotto, Claudio Cremaschini, “First-principle proof of the modified collision boundary conditions for the hard-sphere system”, Physics Letters A, 2014
Demers M.F., Zhang H.-K., “Spectral Analysis of Hyperbolic Systems with Singularities”, Nonlinearity, 27:3 (2014), 379–433
E. J. Torres-Herrera, L.F.. Santos, “Local quenches with global effects in interacting quantum systems”, Phys. Rev. E, 89:6 (2014)
Yurong Li, Jiong Sun, Siqin Yao, “A Class of Generalized Differential Operators with Infinitely Many Discontinuous Points”, Abstract and Applied Analysis, 2014 (2014), 1
Françoise Pène, “Self-intersections of trajectories of the Lorentz process”, DCDS-A, 34:11 (2014), 4781
Jorge Kurchan, “Large deviations, metastability and selection”, Physica A: Statistical Mechanics and its Applications, 2014
A.J.onathan Vidgop, Itzhak Fouxon, “Emergence of distinguishability of patterns of collisions of particles in a non-equilibrium chaotic system”, Physica A: Statistical Mechanics and its Applications, 2014
Germán Sierra, “The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime”, J. Phys. A: Math. Theor, 47:32 (2014), 325204
Dmitry V. Turaev, Christopher Warner, Sergey Zelik, “Energy Growth for a Nonlinear Oscillator Coupled to a Monochromatic Wave”, Regul. Chaotic Dyn., 19:4 (2014), 513–522
Massimo Tessarotto, Claudio Cremaschini, “The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system”, Eur. Phys. J. Plus, 129:7 (2014)
C.P.. Dettmann, “Diffusion in the Lorentz Gas”, Commun. Theor. Phys, 62:4 (2014), 521
A.K.. Behera, A. N. Sekar Iyengar, P.K.. Panigrahi, “Non-stationary dynamics in the bouncing ball: A wavelet perspective”, Chaos, 24:4 (2014), 043107
А. И. Буфетов, Б. М. Гуревич, К. М. Ханин, Ф. Челларози, “Присуждение Я. Г. Синаю премии Абеля”, УМН, 69:5(419) (2014), 167–190 ; A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956
Massimo Tessarotto, Claudio Cremaschini, “Modified BBGKY hierarchy for the hard-sphere system”, Eur. Phys. J. Plus, 129:11 (2014)
Dettmann C.P., “Diffusion in the Lorentz Gas”, Commun. Theor. Phys., 62:4 (2014), 521–540
Massimo Tessarotto, Claudio Cremaschini, “Theory of collisional invariants for the Master kinetic equation”, Physics Letters A, 2015
Massimo Tessarotto, Claudio Cremaschini, “Axiomatic foundations of entropic theorems for hard-sphere systems”, Eur. Phys. J. Plus, 130:5 (2015)
L.A.. Bunimovich, L.V.. Vela-Arevalo, “Some new surprises in chaos”, Chaos, 25:9 (2015), 097614
Kushal Shah, Vassili Gelfreich, Vered Rom-Kedar, Dmitry Turaev, “Leaky Fermi accelerators”, Phys. Rev. E, 91:6 (2015)
B. Fačkovec, E. Vanden-Eijnden, D. J. Wales, “Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling”, J. Chem. Phys, 143:4 (2015), 044119
A. V. Artemyev, A. I. Neishtadt, “Violation of adiabaticity in magnetic billiards due to separatrix crossings”, Chaos, 25:8 (2015), 083109
M.F.. Correia, Hong-Kun Zhang, “Stability and ergodicity of moon billiards”, Chaos, 25:8 (2015), 083110
Dolgopyat D. Nandori P., “Nonequilibrium Density Profiles in Lorentz Tubes With Thermostated Boundaries”, 69, no. 4, 2016, 649–692
В. В. Козлов, “Полиномиальные законы сохранения для газа Лоренца и газа Больцмана–Гиббса”, УМН, 71:2(428) (2016), 81–120 ; V. V. Kozlov, “Polynomial conservation laws for the Lorentz gas and the Boltzmann–Gibbs gas”, Russian Math. Surveys, 71:2 (2016), 253–290
С. В. Болотин, “Вырожденные бильярды”, Современные проблемы механики, Сборник статей, Тр. МИАН, 295, МАИК «Наука/Интерпериодика», М., 2016, 53–71 ; S. V. Bolotin, “Degenerate billiards”, Proc. Steklov Inst. Math., 295 (2016), 45–62
А. П. Маркеев, “Об устойчивости периодических траекторий плоского бильярда Биркгофа”, Современные проблемы механики, Сборник статей, Тр. МИАН, 295, МАИК «Наука/Интерпериодика», М., 2016, 206–217 ; A. P. Markeev, “On the stability of periodic trajectories of a planar Birkhoff billiard”, Proc. Steklov Inst. Math., 295 (2016), 190–201
Manjunath N. Samajdar R. Jain S.R., “A difference-equation formalism for the nodal domains of separable billiards”, Ann. Phys., 372 (2016), 68–73
Jain S.R. Samajdar R., “Nodal Portraits of Quantum Billiards: Domains, Lines, and Statistics”, Rev. Mod. Phys., 89:4 (2017), 045005
Balint P. Nandori P. Szasz D. Toth I.P., “Equidistribution For Standard Pairs in Planar Dispersing Billiard Flows”, Ann. Henri Poincare, 19:4 (2018), 979–1042

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