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ЖУРНАЛЫ // Функциональный анализ и его приложения

Функц. анализ и его прил., 1991, том 25, выпуск 3, страницы 50–69 (Mi faa880)

Новое доказательство формулы Синая для вычисления энтропии гиперболических биллиардов. Приложение к газу Лоренца и стадиону Бунимовича
Н. И. Чернов

Эта публикация цитируется в следующих статьяx:
  1. Amal Al Dowais, Luchezar Stoyanov, “Lyapunov Exponents for Open Billiards in the Exterior of Balls”, SIAM J. Appl. Dyn. Syst., 24:3 (2025), 2139  crossref
  2. Roberto Artuso, Dario Javier Zamora, “Cauchy universality and random billiards”, Phys. Rev. Research, 6:3 (2024)  crossref
  3. Dario Javier Zamora, Roberto Artuso, “Exploring run-and-tumble movement in confined settings through simulation”, The Journal of Chemical Physics, 161:11 (2024)  crossref
  4. Patrick Wright, Jitse Niesen, Rob Sturman, “Rigorous bounds on Lyapunov exponents of linked twist maps”, Nonlinearity, 36:3 (2023), 1699  crossref
  5. George Datseris, Lukas Hupe, Ragnar Fleischmann, “Estimating Lyapunov exponents in billiards”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29:9 (2019)  crossref
  6. Laura Menini, Corrado Possieri, Antonio Tornambè, “Tracking of a Bouncing Ball in a Planar Billiard Through Continuous-Time Approximations”, Journal of Computational and Nonlinear Dynamics, 13:6 (2018)  crossref
  7. Péter Bálint, Thomas Gilbert, Péter Nándori, Domokos Szász, Imre Péter Tóth, “On the Limiting Markov Process of Energy Exchanges in a Rarely Interacting Ball-Piston Gas”, J Stat Phys, 166:3-4 (2017), 903  crossref
  8. Yu.N. Maslovsky, “3D composite particles”, Funct.Mater., 22:1 (2015), 69  crossref
  9. C. Bianca, “On the mathematical transport theory in microporous media: The billiard approach”, Nonlinear Analysis: Hybrid Systems, 4:4 (2010), 699  crossref
  10. Yi-Chiuan Chen, “On topological entropy of billiard tables with small inner scatterers”, Advances in Mathematics, 224:2 (2010), 432  crossref
  11. N. Chernov, H. -K. Zhang, “Improved Estimates for Correlations in Billiards”, Commun. Math. Phys., 277:2 (2007), 305  crossref
  12. Florin P. Boca, Alexandru Zaharescu, “The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit”, Commun. Math. Phys., 269:2 (2006), 425  crossref
  13. Florin P. Boca, Alexandru Zaharescu, Noncommutative Geometry and Number Theory, 2006, 57  crossref
  14. Arseni Goussev, J. R. Dorfman, “Lyapunov spreading of semiclassical wave packets for the Lorentz gas: Theory and applications”, Phys. Rev. E, 71:2 (2005)  crossref
  15. Yi-Chiuan Chen, “Anti-integrability in scattering billiards”, Dynamical Systems, 19:2 (2004), 145  crossref
  16. Eduardo A. Coronado, George C. Schatz, “Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach”, The Journal of Chemical Physics, 119:7 (2003), 3926  crossref
  17. Christian Foltin, “Billiards with positive topological entropy”, Nonlinearity, 15:6 (2002), 2053  crossref
  18. D. Burago, S. Ferleger, A. Kononenko, “Collisions in semi-dispersing billiard on Riemannian manifold”, Topology and its Applications, 122:1-2 (2002), 87  crossref
  19. Н. И. Чернов, “Средняя длина пробега в биллиардных системах”, Матем. просв., сер. 3, 5, МЦНМО, М., 2001, 100–105  mathnet
  20. D. Burago, S. Ferleger, A. Kononenko, Encyclopaedia of Mathematical Sciences, 101, Hard Ball Systems and the Lorentz Gas, 2000, 9  crossref
  21. N. Chernov, Encyclopaedia of Mathematical Sciences, 101, Hard Ball Systems and the Lorentz Gas, 2000, 121  crossref
  22. Pierre Gaspard, “Microscopic chaos and chemical reactions”, Physica A: Statistical Mechanics and its Applications, 263:1-4 (1999), 315  crossref
  23. H. van Beijeren, Arnulf Latz, J. R. Dorfman, “Chaotic properties of dilute two- and three-dimensional random Lorentz gases: Equilibrium systems”, Phys. Rev. E, 57:4 (1998), 4077  crossref
  24. A. Latz, “Lyapunov spectrum of a random Lorentz gas in a magnetic field”, Z. Phys. B, 103:3 (1997), 351  crossref
  25. H. S. Dumans, L. Dumas, F. Golse, “Remarks on the notion of mean free path for a periodic array of spherical obstacles”, J Stat Phys, 87:3-4 (1997), 943  crossref
  26. Mohammed Lach-hab, Estela Blaisten-Barojas, T. Sauer, “Irregular scattering of particles confined to ring-bounded cavities”, J Stat Phys, 87:1-2 (1997), 137  crossref
  27. Per Dahlqvist, “The Lyapunov exponent in the Sinai billiard in the small scatterer limit”, Nonlinearity, 10:1 (1997), 159  crossref
  28. A. Latz, H. van Beijeren, J. R. Dorfman, “Lyapunov Spectrum and the Conjugate Pairing Rule for a Thermostatted Random Lorentz Gas: Kinetic Theory”, Phys. Rev. Lett., 78:2 (1997), 207  crossref
  29. N. Chernov, “Entropy, Lyapunov exponents, and mean free path for billiards”, J Stat Phys, 88:1-2 (1997), 1  crossref
  30. 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  crossref
  31. P. L. Garrido, “Kolmogorov–Sinai Entropy, Lyapunov Exponents, and Mean Free Time in Billiard Systems”, Journal of Statistical Physics, 88:3-4 (1997), 807  crossref
  32. Artur Lopes, Roberto Markarian, “Open Billiards: Invariant and Conditionally Iinvariant Probabilities on Cantor Sets”, SIAM J. Appl. Math., 56:2 (1996), 651  crossref
  33. N. I. Chernov, S. Troubetzkoy, “Measures with infinite Lyapunov exponents for the periodic Lorentz gas”, J Stat Phys, 83:1-2 (1996), 193  crossref
  34. N. I. Chernov, C. Haskell, “Nonuniformly hyperbolic K-systems are Bernoulli”, Ergod. Th. Dynam. Sys., 16:1 (1996), 19  crossref
  35. Per Dahlqvist, “Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions”, J Stat Phys, 84:3-4 (1996), 773  crossref
  36. Henk van Beijeren, J. R. Dorfman, “Lyapunov Exponents and Kolmogorov-Sinai Entropy for the Lorentz Gas at Low Densities”, Phys. Rev. Lett., 74:22 (1995), 4412  crossref
  37. A. Hakmi, F. Bosco, I. Antoniou, “First return map of the periodic Lorentz gas”, Phys. Rev. E, 51:5 (1995), 3952  crossref
  38. N. Chernov, R. Markarian, “Entropy of non-uniformly hyperbolic plane billiards”, Bol. Soc. Bras. Mat, 23:1-2 (1992), 121  crossref
  39. Domokos Szász, “On theK-property of some planar hyperbolic billiards”, Commun.Math. Phys., 145:3 (1992), 595  crossref


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