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Uspekhi Mat. Nauk, 1995, Volume 50, Issue 1(301), Pages 143–186 (Mi umn1042)  

This article is cited in 27 scientific papers (total in 29 papers)

Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism

L. D. Pustyl'nikov

All-Russian Scientific Research Institute Power Industry

Full text: PDF file (508 kB)
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English version:
Russian Mathematical Surveys, 1995, 50:1, 145–189

Bibliographic databases:

UDC: 517.938+536.75+531.395
MSC: 82C05, 82C35
Received: 18.08.1993

Citation: L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Uspekhi Mat. Nauk, 50:1(301) (1995), 143–186; Russian Math. Surveys, 50:1 (1995), 145–189

Citation in format AMSBIB
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\by L.~D.~Pustyl'nikov
\paper Poincar\'e models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism
\jour Uspekhi Mat. Nauk
\yr 1995
\vol 50
\issue 1(301)
\pages 143--186
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\transl
\jour Russian Math. Surveys
\yr 1995
\vol 50
\issue 1
\pages 145--189
\crossref{https://doi.org/10.1070/RM1995v050n01ABEH001663}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. D. Pustyl'nikov, “Infinite-dimensional non-linear ordinary differential equations and the KAM theory”, Russian Math. Surveys, 52:3 (1997), 551–604  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. J. Dittrich, P. Duclos, N. Gonzalez, “Stability and Instability of the Wave Equation Solutions in a Pulsating Domain”, Rev. Math. Phys, 10:07 (1998), 925  crossref
    3. T. Krüger, L. D. Pustyl'nikov, S. Troubetzkoy, “The nonautonomous function-theoretic center problem”, Bol Soc Bras Mat, 30:1 (1999), 1  crossref  mathscinet
    4. L. D. Pustyl'nikov, “The law of entropy increase and generalized billiards”, Russian Math. Surveys, 54:3 (1999), 650–651  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Deryabin, MV, “Generalized relativistic billiards”, Regular & Chaotic Dynamics, 8:3 (2003), 283  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Deryabin, MV, “On generalized relativistic billiards in external force fields”, Letters in Mathematical Physics, 63:3 (2003), 195  crossref  mathscinet  zmath  isi  elib
    7. M.V. Deryabin, L.D. Pustyl’nikov, “Exponential Attractors in Generalized Relativistic Billiards”, Comm Math Phys, 248:3 (2004), 527  crossref  mathscinet  adsnasa  isi  elib
    8. L. D. Pustylnikov, “Dinamicheskie sistemy s uprugimi otrazheniyami i mekhanizm uskoreniya Fermi”, Matem. prosv., ser. 3, 8, Izd-vo MTsNMO, M., 2004, 164–180  mathnet
    9. L. D. Pustylnikov, “Geometricheskaya zadacha, svyazannaya s obobschennymi billiardami”, Matem. prosv., ser. 3, 9, Izd-vo MTsNMO, M., 2005, 86–92  mathnet
    10. L. D. Pustyl'nikov, “Generalized Newtonian periodic billiards in a ball”, Russian Math. Surveys, 60:2 (2005), 365–366  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Mikhail V. Deryabin, Lev D. Pustyl’nikov, “Nonequilibrium Gas and Generalized Billiards”, J Statist Phys, 126:1 (2007), 117  crossref  mathscinet  zmath  isi  elib
    12. A. Yu. Loskutov, “Dynamical chaos: systems of classical mechanics”, Phys. Usp., 50:9 (2007), 939–964  mathnet  crossref  crossref  adsnasa  isi  elib
    13. ALEXANDER LOSKUTOV, OLGA CHICHIGINA, ALEXEI RYABOV, “THERMODYNAMICS OF DISPERSING BILLIARDS WITH TIME-DEPENDENT BOUNDARIES”, Int. J. Bifurcation Chaos, 18:09 (2008), 2863  crossref
    14. S Dorbolo, F Ludewig, N Vandewalle, “Bouncing trimer: a random self-propelled particle, chaos and periodical motions”, New J Phys, 11:3 (2009), 033016  crossref  isi
    15. Jeong-Bo Shim, Mahir S. Hussein, Martina Hentschel, “Numerical test of Born–Oppenheimer approximation in chaotic systems”, Physics Letters A, 373:39 (2009), 3536  crossref
    16. A. Yu. Loskutov, “Fascination of chaos”, Phys. Usp., 53:12 (2010), 1257–1280  mathnet  crossref  crossref  isi  elib
    17. A. Yu. Loskutov, A. B. Ryabov, A. K. Krasnova, O. A. Chichigina, “Bilyardy s vozmuschaemymi granitsami i nekotorye ikh svoistva”, Nelineinaya dinam., 6:3 (2010), 573–604  mathnet  elib
    18. 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  crossref
    19. Rafael S. Pinto, Patricio S. Letelier, “Fermi Acceleration in driven relativistic billiards”, Physics Letters A, 2011  crossref
    20. Alexander Loskutov, Olga Chichigina, Alexandra Krasnova, Igor M. Sokolov, “Superdiffusion in 2D open-horizon billiards with stochastically oscillating boundaries”, Europhys Lett EPL, 98:1 (2012), 10006  crossref
    21. V. Gelfreich, V. Rom-Kedar, D. Turaev, “Fermi acceleration and adiabatic invariants for non-autonomous billiards”, Chaos, 22:3 (2012), 033116  crossref
    22. Stefano Marò, “Coexistence of bounded and unbounded motions in a bouncing ball model”, Nonlinearity, 26:5 (2013), 1439  crossref
    23. Diogo Ricardo da Costa, D.F..M. Oliveira, E.D.. Leonel, “Dynamical and statistical properties of a rotating oval billiard”, Communications in Nonlinear Science and Numerical Simulation, 2013  crossref
    24. L. D. Pustylnikov, M. V. Deryabin, “Chërnye dyry i obobschënnye relyativistskie billiardy”, Preprinty IPM im. M. V. Keldysha, 2013, 054, 36 pp.  mathnet
    25. L. D. Pustyl'nikov, M. V. Deryabin, “Nonequilibrium gas, entropy and generalized billiards”, Preprinty IPM im. M. V. Keldysha, 2014, 003, 10 pp.  mathnet
    26. Stefano Marò, “Chaotic Dynamics in an Impact Problem”, Ann. Henri Poincaré, 2014  crossref
    27. A. Benseghir, W. A. T. Wan Abdullah, B. B. Baizakov, F. Kh. Abdullaev, “Matter-wave soliton bouncing on a reflecting surface under the effect of gravity”, Phys. Rev. A, 90:2 (2014)  crossref
    28. V. D. Vinokurova, N. N. Rosanov, “The Fermi-Ulam problem and sticking mode”, Tech. Phys. Lett, 40:11 (2014), 946  crossref
    29. Kushal Shah, Vassili Gelfreich, Vered Rom-Kedar, Dmitry Turaev, “Leaky Fermi accelerators”, Phys. Rev. E, 91:6 (2015)  crossref
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