Big islands in dispersing billiard-like potentials

Physica D: Nonlinear Phenomena

Volumn 130, Issue 3-4, 1999, Pages 187-210

  Rom Kedar, Vered ^a,c   Turaev, Dmitry ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

Elliptic islands; Ergodicity; Mixed dynamics; Singular Hamiltonian systems

Indexed keywords

EID: 0346703292     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00021-4     Document Type: Article

References (23)

1. H. Poincaré, Sur les équations de la dynamique et le problème de trois corps, Acta Math. 13 (1890) 1-270.
2. D.V. Anosov, Geodesic flows on Riemann manifolds with negative curvature, Proc. Steklov Inst. Math., 90, 1967.
3. Y. Sinai, Dynamical systems with elastic reflections: Ergodic properties of scattering billiards, Russian Math. Sur. 25(1) (1970) 137-189.
4. Y. Sinai, N. Chernov, Ergodic properties of certain systems of two-dimensional disks and three-dimensional balls, Russ. Math. Surv. 42(3) (1987) 181-207.
5. G. Gallavotti, D. Ornstein, Billiards and Bernoulli schemes, Comm. Math. Phys. 38 (1974) 83-101.
6. D. Szász, Boltzmann's ergodic hypothesis, a conjecture for centuries? Studia Sci. Math. Hungar. 31 (1-3) (1996) 299-322.
7. D. Turaev, V. Rom-Kedar, Islands appearing in near-ergodic flows, Nonlinearity 11(3) (1998) 575-600.
8. V. Donnay, Elliptic islands in generalized Sinai billiards, Ergod. Th. Dynam. Sys. 16 (1996) 975-1010.
9. C. Karney, Long time correlations in the stochastic regime, Physica D 8 (1983) 360.
10. G. Zaslavsky, M. Edelman, B. Niyazov, Self-similarity, renormalization and phase space nonuniformity of hamiltonian chaotic dynamics, Chaos 7 (1997) 159.
11. P. Duarte, Plenty of elliptic islands for the standard family of area preserving maps, Ann. Inst. H. Poincaré Anal. Non Liniaire 11 (4) (1994) 359-409.
12. R. MacKay, J. Meiss, I. Percival, Resonances in area preserving maps, Physica D 27 (1987) 1-20.
13. J. Meiss, E. Ott, Markov tree model of transport in area-preserving maps, Physica D 20 (1986) 387-402.
14. R. Fleischmann, T. Geisel, R. Ketzmerick, Quenched and negative hall effect in periodic media: application to antidot superlattices, Europhys. lett. 25(3) (1994) 219-224.
15. G. Zaslavsky, M. Edelman, Maxwell's demon as a dynamical model, Phys. Rev. E 56(5) (1997) 5310-5320.
16. W.L. Ditto, K. Showalter, Focus issue on control and synchronization of Chaos, Chaos 7(4) (1997) 509-687.
17. C. Liverani, Decay of correlations, Annals of Mathematics 142 (1995) 239-301.
18. K. Hansen, Bifurcations and complete chaos for the diamagnetic kepler problem, Phys. Rev. E 51(3) (1995) 1838-1844.
19. P. Collas, D. Klein, H.-P. Schwebler, Convergence of Hamiltonian systems to billiards, Chaos (1998).
20. V. Biragov, Bifurcations in a two-parameter family of conservative mappings that are close to the Henon map, Selecta. Mat. Sovietica. 9 (1990) 247-280.
21. A.I. Neishtadt, V.V. Sidorenko, D.V. Treschev, Stable periodic motions in the problem on passage through a separatrix, Chaos 7(1) (1997) 2-11.
22. Y. Sinai, On the foundations of the ergodic hypothesis for dynamical system of statistical mechanics, Dokl. Akad. Nauk. SSSR 153 (1963) 1261-1264.
23. M. Wojtkowski, Principles for the design of billiards with nonvanishing lyapunov exponents, Comm. Math. Phys. 105(3) (1986) 391-414.