Billiards with polynomial mixing rates

Nonlinearity

Volumn 18, Issue 4, 2005, Pages 1527-1553

  Chernov, N ^a   Zhang, H K ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21244475162     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/4/006     Document Type: Article

References (25)

1. Balint P and Toth I P 2003 Correlation decay in certain soft billiards Commun. Math. Phys. 243 55-91
2. Balint P, Chernov N, Szasz D and Toth I P 2003 Geometry of multidimensional dispersing billiards Asterisque 286 119-50
3. Bunimovich L A 1974 On billiards close to dispersing Math. USSR Sbornik. 23 45-67
4. Bunimovich L A 1979 On the ergodic properties of nowhere dispersing billiards Commun. Math. Phys. 65 295-312
5. Bunimovich L A 1990 On Absolutely Focusing Mirrors (Lecture Notes in Mathematics vol 1514) (New York: Springer) pp 62-82
6. Bunimovich L A, Sinai Ya G and Chernov N I 1990 Markov partitions for two-dimensional hyperbolic billiards Russ. Math. Surv. 45 105-52
7. Bunimovich L A, Sinai Ya G and Chernov N I 1991 Statistical properties of two-dimensional hyperbolic billiards Russ. Math. Surv. 46 47-106
8. Chernov N 1997 Entropy, Lyapunov exponents and mean-free path for billiards J. Stat. Phys. 88 1-29
9. Chernov N 1999 Decay of correlations in dispersing billiards J. Stat. Phys. 94 513-56
10. Chernov N 2001 Sinai billiards under small external forces Ann. H Poincaré 2 197-236
11. Chernov N and Markarian R 2003 Introduction to the Ergodic Theory of Chaotic Billiards 2nd edn (Rio, Brazil: IMPA)
12. Chernov N and Young L-S 2000 Decay of correlations for Lorentz gases and hard balls Hard Ball Systems and the Lorentz Gas (Encyclopaedia of Mathematical Sciences vol 101) ed D Szasz (Berlin: Springer) pp 89-120
13. Donnay V 1991 Using integrability to produce chaos: billiards with positive entropy Commun. Math. Phys. 141 225-57
14. Gallavotti G and Ornstein D 1974 Billiards and Bernoulli schemes Commun. Math. Phys. 38 83-101
15. Szasz D (ed) 2000 Hard Ball Systems and the Lorentz Gas (Encyclopaedia of Mathematical Sciences vol 101) (Berlin: Springer)
16. Katok A and Strelcyn J-M 1986 Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities (Lecture Notes in Mathematics vol 1222) (New York: Springer)
17. Machta J 1983 Power law decay of correlations in a billiard problem J. Stat. Phys. 32 555-64
18. Markarian R 1988 Billiards with Pesin region of measure one Commun. Math. Phys. 118 87-97
19. Markarian R 2004 Billiards with polynomial decay of correlations Ergod. Theory Dynam. Syst. 24 177-97
20. Sarig O 2002 Subexponential decay of correlations Invent. Math. 150 629-53
21. Sinai Ya G 1970 Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards Russ. Math. Surv. 25 137-89
22. Vivaldi F, Casati G and Guarneri I 1983 Origin of long-time tails in strongly chaotic systems Phys. Rev. Lett. 51 727-30
23. Wojtkowski M P 1986 Principles for the design of billiards with nonvanishing Lyapunov exponents Commun. Math. Phys. 105 391-414
24. Young L-S 1998 Statistical properties of systems with some hyperbolicity including certain billiards Ann. Math. 147 585-650
25. Young L-S 1999 Recurrence times and rates of mixing Israel J. Math. 110 153-88