Sinai billiards under small external forces

Annales Henri Poincare

Volumn 2, Issue 2, 2001, Pages 197-236

  Chernov, N I ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035532207     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001034     Document Type: Article

References (22)

1. P. Bleher, Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon, J. Statist. Phys. 66, 315-373 (1992).
2. L. A. Bunimovich, Ya. G. Sinai and N.I. Chernov, Markov partitions for two-dimensional billiards, Russ. Math. Surv. 45, 105-152 (1990).
3. L. A. Bunimovich, Ya. G. Sinai and N. I. Chernov, Statistical properties of two-dimensional hyperbolic billiards, Russ. Math. Surv. 46, 47-106 (1991).
4. N. I. Chernov, G. L. Eyink, J. L. Lebowitz and Ya. G. Sinai, Steady-state electrical conduction in the periodic Lorentz gas, Comm. Math. Phys. 154, 569-601 (1993).
5. N. I. Chernov, G. L. Eyink, J. L. Lebowitz and Ya. G. Sinai, Derivation of Ohm's law in a deterministic mechanical model, Phys. Rev. Let. 70, 2209-2212 (1993).
6. N. Chernov, Statistical properties of piecewise smooth hyperbolic systems in high dimensions, Discr. Cont. Dynam. Syst. 5, 425-448 (1999).
7. N. Chernov, Decay of correlations and dispersing billiards, J. Statist. Phys. 94, 513-556 (1999).
8. C. P. Dettmann and G. P. Morriss, Crisis in the periodic Lorentz gas, Phys. Rev. E. 54, 4782-4790 (1996).
9. B. Friedman, R. F. Martin, Decay of the velocity autocorrelation function for the periodic Lorentz gas, Phys. Lett. A 105, 23-26 (1984).
10. B. Friedman, R. F. Martin, Behavior of the velocity autocorrelation function for the periodic Lorentz gas, Physica D 30, 219-227 (1988).
11. G. Gallavotti and D. Ornstein, Billiards and Bernoulli schemes, Comm. Math. Phys. 38, 83-101 (1974).
12. G. Gallavotti and E.D.G. Cohen, Dynamical ensembles in stationary states, J. Stat. Phys. 80, 931-970 (1995).
13. N. van Kampen The Case Against Linear Response Theory, Phys. Norv. 5, 279-284 (1971).
14. Ya. B. Pesin, Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties, Ergod. Th. Dynam. Sys. 12, 123-151 (1992).
15. D. Ruelle, Smooth dynamics and new theoretical ideas in non-equilibrium statistical mechanics, J. Statist. Phys. 94 (1999).
16. E. A. Sataev, Invariant measures for hyperbolic maps with singularities, Russ. Math. Surv. 47, 191-251 (1992).
17. Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surv. 25, 137-189 (1970).
18. M. P. Wojtkowski, Invariant families of cones and Lyapunov exponents, Ergod. Th. Dynam. Sys. 5, 145-161 (1985).
19. M. P. Wojtkowski, Magnetic flows and Gaussian thermostats on manifolds of negative curvature, Fund. Math. 163, 177-191 (2000).
20. M. P. Wojtkowski, Flows on Weyl manifolds and Gaussian thermostats, preprint (2000).
21. L.S. Young, Statistical properties of dynamical systems with some hyperbolicity, Annals of Math. 147, 585-650 (1998).
22. L.-S. Young, Ergodic theory of chaotic dynamical systems, XIIth International Congress of Mathematical Physics (ICMP'97) (Brisbane), 131-143, Internat. Press, Cambridge, MA, 1999.