Flow-invariant hypersurfaces in semi-dispersing billiards

Annales Henri Poincare

Volumn 8, Issue 3, 2007, Pages 475-483

  Chernov, Nikolai ^a   Simányi, Nandor ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

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Indexed keywords

EID: 34547280408     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-006-0313-5     Document Type: Article

References (21)

1. P. Balint, N. Chernov, D. Szasz, and I. P. Toth, Multi-dimensional semi-dispersing billiards: singularities and the fundamental theorem, Ann. H. Poincaré 3 (2002), 451-482.
2. P. Balint, N. Chernov, D. Szasz, and I. P. Toth, Geometry of multidimensional dispersing billiars, Astérisque 286 (2003), 119-150.
3. N. Chernov, Statistical properties of the periodic Lorentz gas. Multidimensional case, J. Stat. Phys. 74 (1994), 11-53.
4. A. Katok and K. Burns, Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems, Ergod. Th. Dyn. Syst. 14 (1994), 757-785.
5. A. Krámli, N. Simányi & D. Szász, A "transversal" fundamental theorem for semi-dispersing billiards, Comm. Math. Phys. 129 (1990), 535-560
6. A. Krámli, N. Simányi &: D. Szász, The K-property of three billiard balls, Ann. Math. 133 (1991), 37-72
7. A. Krámli, N. Simányi &: D. Szász, The K-property of four billiard balls, Comm. Math. Phys. 144 (1992), 107-142.
8. C. Liverani and M. Wojtkowski, Ergodicity in Hamiltonian systems, Dynamics reported, Dynam. Report. Expositions Dynam. Systems (N.S.) 4, Springer, Berlin (1995), 130-202.
9. N. Simányi, The K-property of N billiard balls I, Invent. Math. 108 (1992), 521-548.
10. N. Simányi, The K-property of N billiard balls II, Invent. Math. 110 (1992), 151-172.
11. N. Simányi & D. Szász, Hard ball systems are completely hyperbolic, Ann. Math. 149 (1999), 35-96.
12. N. Simányi, The Complete hyperbolicity of cylindric billiards, Ergod. Th. Dynam. Syst. 22 (2002), 281-302.
13. N. Simányi Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems, Invent. Math. 154 (2003), 123-178.
14. N. Simányi Proof of the ergodic hypothesis for typical hard ball systems, Ann. H. Poincaré 5 (2004), 203-233.
15. Ya. G. Sinai, On the foundation of the ergodic hypothesis for a dynamical system of statistical mechanics, Dokl. Akad. Nauk SSSR, 153 (1963), 1261-1264.
16. Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surv. 25 (1970), 137-189.
17. Ya. G. Sinai, Development of Krylov's ideas, Afterword to N.S. Krylov, Works on the foundations of statistical physics. Princeton U. Press, Princeton, N. J. (1979), 239-281.
18. Ya. G. Sinai and N. I. Chernov, Entropy of a gas of hard spheres with respect to the group of space-time translations, Trudy Sem. Petrovskogo, 8 (1982), 218-238 (in Russian),
19. and in: Dynamical Systems, Ed. by Ya. Sinai, Adv. Series in Nonlin. Dynam. 1, 373-390 (in English).
20. Ya. G. Sinai and N. I. Chernov, unpublished manuscript, a draft version of [20].
21. Ya. G. Sinai and N. I. Chernov, Ergodic properties of some systems of 2-dimensional discs and 3-dimensional, spheres, Russ. Math. Surv. 42 (1987), 181-207.