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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 1(5), Pages 49–73 (Mi msb3632)  

This article is cited in 33 scientific papers (total in 34 papers)

On billiards close to dispersing

L. A. Bunimovich


Abstract: One considers dynamical systems generated by billiards which are “perturbations” of dispersing billiards. It is shown that such dynamical systems are systems of A. N. Kolmogorov ($K$-systems), if the “perturbation” satisfies certain conditions which have an intuitive geometric interpretation.
Bibliography: 12 titles.

Full text: PDF file (2423 kB)
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English version:
Mathematics of the USSR-Sbornik, 1974, 23:1, 45–67

Bibliographic databases:

UDC: 519.2
MSC: Primary 28A65; Secondary 54H20, 58F15
Received: 06.03.1973

Citation: L. A. Bunimovich, “On billiards close to dispersing”, Mat. Sb. (N.S.), 94(136):1(5) (1974), 49–73; Math. USSR-Sb., 23:1 (1974), 45–67

Citation in format AMSBIB
\Bibitem{Bun74}
\by L.~A.~Bunimovich
\paper On billiards close to dispersing
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 1(5)
\pages 49--73
\mathnet{http://mi.mathnet.ru/msb3632}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=342677}
\zmath{https://zbmath.org/?q=an:0309.58018}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 1
\pages 45--67
\crossref{https://doi.org/10.1070/SM1974v023n01ABEH001713}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
    2. O Penrose, Rep Prog Phys, 42:12 (1979), 1937  crossref  adsnasa  isi
    3. George M. Zaslavsky, “Stochasticity in quantum systems”, Physics Reports, 80:3 (1981), 157  crossref  elib
    4. L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Markov partitions for two-dimensional hyperbolic billiards”, Russian Math. Surveys, 45:3 (1990), 105–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. N. I. Chernov, “Topological entropy and periodic points of two-dimensional hyperbolic billiards”, Funct. Anal. Appl., 25:1 (1991), 39–45  mathnet  crossref  mathscinet  zmath  isi
    6. 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  mathnet  crossref  mathscinet  zmath  isi
    7. L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Statistical properties of two-dimensional hyperbolic billiards”, Russian Math. Surveys, 46:4 (1991), 47–106  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. S. E. Trubetskoi, “Stochastic stability of dispersing billiards”, Theoret. and Math. Phys., 86:2 (1991), 151–158  mathnet  crossref  mathscinet  isi
    9. N. Chernov, R. Markarian, “Entropy of non-uniformly hyperbolic plane billiards”, Bol Soc Bras Mat, 23:1-2 (1992), 121  crossref  mathscinet  zmath
    10. Bunimovich L., “On Absolutely Focusing Mirrors”, Lect. Notes Math., 1514 (1992), 62–82  isi
    11. R Markarian, Nonlinearity, 6:5 (1993), 819  crossref  mathscinet  zmath  isi
    12. Roberto Markarian, “Statistical properties of dynamical systems with singularities”, J Statist Phys, 80:5-6 (1995), 1207  crossref  mathscinet  zmath
    13. Roberto Markarian, Sylvie Oliffson Kamphorst, Sônia Pinto Carvalho, “Chaotic properties of the elliptical stadium”, Comm Math Phys, 174:3 (1996), 661  crossref  mathscinet  zmath
    14. N. Chernov, “Entropy, Lyapunov exponents, and mean free path for billiards”, J Statist Phys, 88:1-2 (1997), 1  crossref  mathscinet  zmath  adsnasa
    15. N Chernov, S Troubetzkoy, Nonlinearity, 11:4 (1998), 1095  crossref  mathscinet  zmath  isi
    16. L.R. Arnaut, “Operation of electromagnetic reverberation chambers with wave diffractors at relatively low frequencies”, IEEE Trans Electromagn Compat, 43:4 (2001), 637  crossref  isi
    17. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. L. A. Bunimovich, “Rasseyanie, defokusirovka i astigmatizm”, Matem. prosv., ser. 3, 5, MTsNMO, M., 2001, 106–124  mathnet
    19. Deryabin M., Pustyl'nikov L., “Exponential Attractors in Generalized Relativistic Billiards”, Commun. Math. Phys., 248:3 (2004), 527–552  crossref  isi
    20. N Chernov, H-K Zhang, “Billiards with polynomial mixing rates”, Nonlinearity, 18:4 (2005), 1527  crossref  mathscinet  zmath  isi
    21. E. Akalin, M.U. Akhmet, “The principles of B-smooth discontinuous flows”, Computers & Mathematics with Applications, 49:7-8 (2005), 981  crossref
    22. R Egydio de Carvalho, F Caetano de Souza, Edson D Leonel, “Fermi acceleration on the annular billiard: a simplified version”, J Phys A Math Gen, 39:14 (2006), 3561  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. N. Chernov, H. -K. Zhang, “Improved Estimates for Correlations in Billiards”, Comm Math Phys, 277:2 (2007), 305  crossref  mathscinet  adsnasa  isi
    24. N. Chernov, H. -K. Zhang, “Regularity of Bunimovich’s stadia”, Reg Chaot Dyn, 12:3 (2007), 335  crossref  mathscinet  isi
    25. Edson D. Leonel, “Corrugated Waveguide under Scaling Investigation”, Phys Rev Letters, 98:11 (2007), 114102  crossref  isi
    26. A. Yu. Loskutov, “Dynamical chaos: systems of classical mechanics”, Phys. Usp., 50:9 (2007), 939–964  mathnet  crossref  crossref  adsnasa  isi  elib
    27. L BUSSOLARI, M LENCI, “Hyperbolic billiards with nearly flat focusing boundaries, I”, Physica D: Nonlinear Phenomena, 237:18 (2008), 2272  crossref
    28. L. A. Bunimovich, “Criterion of absolute focusing for focusing component of billiards”, Reg Chaot Dyn, 14:1 (2009), 42  crossref  mathscinet  isi
    29. A. B. Kapranova, “Metod opredeleniya koeffitsienta makrodiffuzii v protsesse smesheniya tverdykh dispersnykh sred v tsentrobezhnom apparate”, Matem. modelirovanie, 21:3 (2009), 83–94  mathnet  zmath
    30. 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
    31. Hong-Kun Zhang, “MIXING RATE FOR RECTANGULAR BILLIARDS WITH DIAMOND RECTANGLES”, American Journal of Mathematical and Management Sciences, 30:1-2 (2010), 53  crossref
    32. Hong-Kun Zhang, “Estimates for correlations in billiards with large arcs”, Acta Math. Appl. Sin. Engl. Ser, 27:3 (2011), 381  crossref
    33. Tarshis M.Yu., Volkov M.V., Zaitsev A.I., “K raschetu barabannykh smesitelei sypuchikh materialov s dopolnitelnymi rabochimi elementami”, Izvestiya vysshikh uchebnykh zavedenii. seriya: khimiya i khimicheskaya tekhnologiya, 55:12 (2012), 108–110  elib
    34. Gianluigi Del Magno, Roberto Markarian, “Singular Sets of Planar Hyperbolic Billiards are Regular”, Regul. Chaotic Dyn., 18:4 (2013), 425–452  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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