Elliptic islands appearing in near-ergodic flows

Nonlinearity

Volumn 11, Issue 3, 1998, Pages 575-600

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

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007679077     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/11/3/010     Document Type: Article

References (40)

1. Baldwin P R 1988 Soft billiard systems J. Phys. D: Appl. Phys. 29 321-42
2. Broomhead D S and Gutkin E 1993 The dynamics of billiards with no-slip collisions J. Phys. D: Appl. Phys. 67 188-97
3. Bunimovich L and Sinai Y 1973 The fundamental theorem of the theory of scattering billiards Mat. Sb. (N.S.) 90 415-31 (in Russian)
4. Bunimovich L and Sinai Y 1980 Markov partitions for dispersed billiards Commun. Math. Phys. 78 247-80
5. Bunimovich L, Sinai Y and Chernov N 1990 Markov partitions for two-dimensional hyperbolic billiards Usp. Mat. Nauk 45 97-134, 221 (Engl. transl.) 1990 Russ. Math. Surv. 45 105-52
6. Bunimovich L, Sinai Y and Chernov N 1990 Markov partitions for two-dimensional hyperbolic billiards Usp. Mat. Nauk 45 97-134, 221 (Engl. transl.) 1990 Russ. Math. Surv. 45 105-52
7. Bunimovich L, Sinai Y and Chernov 1991 Statistical properties of two-dimensional hyperbolic billiards Usp. Mat. Nauk 46 43-92, 192 (Engl. transl.) 1991 Russ. Math. Surv. 46 47-106
8. Bunimovich L, Sinai Y and Chernov 1991 Statistical properties of two-dimensional hyperbolic billiards Usp. Mat. Nauk 46 43-92, 192 (Engl. transl.) 1991 Russ. Math. Surv. 46 47-106
9. Bunimovich L A 1985 Decay of correlations in dynamical systems with chaotic behavior Zh. Eksp. Teor. Fiz 89 1452-71 (Engl. transl.) Sov. Phys.-JETP 62 842-52
10. Bunimovich L A 1985 Decay of correlations in dynamical systems with chaotic behavior Zh. Eksp. Teor. Fiz 89 1452-71 (Engl. transl.) Sov. Phys.-JETP 62 842-52
11. Constantin P, Grossman E and Mungan M 1995 Inelastic collisions of three particles on a line as a two-dimensional billiard Physica D 83 409-20
12. Cornfeld I P, Fomin S V and Sinai Y G 1982 Ergodic theory Fundamental Principles of Mathematical Science vol 245, translated from the Russian by A B Sosinskiǐ(Berlin: Springer)
13. Donnay V 1996 Elliptic islands in generalized sinai billiards Ergod. Theor. Dynam. Syst. 16 975-1010
14. Donnay V and Liverani C 1991 Potentials on the two-torus for which the Hamiltonian flow is ergodic Commun. Math. Phys. 135 267-302
15. DSTOOLS Computer program. Cornell University, center of applied mathematics (Ithaca, NY: Cornell University Press)
16. Gallavotti G and Ornstein D 1974 Billiard and Bernoulli schemes Commun. Math. Phys. 38 83-101
17. Gavrilov N and Shilnikov L 1972 On three dimensional dynamical systems close to systems with a structurally unstable homoclinic curve I Math. USSR Sb. 88 467-85
18. Gonchenko S V, Shilnikov L P and Turaev D V 1996 Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits Chaos 6 15-31
19. Guckenheimer J and Holmes P 1983 Non-linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer)
20. Gutkin E 1996 Billiards in polygons: survey of recent results J. Stat. Phys. 83 7-26
21. Gutzwiller M 1990 Chaos in Classical and Quantum Mechanic (New York: Springer)
22. Hansen K 1995 Bifurcations and complete chaos for the diamagnetic kepler problem Phys. Rev. E 51 1838-44
23. Jakobson M 1981 Absolutely continuous invariant measures for one parameter families of one-dimensional maps Commun. Math. Phys. 81 39-88
24. Katok A and Hasselblatt B 1995 Introduction to the modern theory of dynamical systems Encyclopedia of Mathematics and its Applications vol 54 (Cambridge: Cambridge University Press)
25. Katok A B, Strelcyn J M, Ledrappier F and Przytycki F 1986 Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities vol 1222 (Berlin: Springer)
26. Knauf A 1989 On soft billiard systems J. Phys. D: Appl. Phys. 36 259-62
27. Kubo I 1976 Perturbed billiard systems i the ergodicity of the motion of a particle in a compound central field Nagoya Math. J. 61 1-57
28. Kubo I and Murata H 1981 Perturbed billiard systems II Bernoulli properties Nagoya Math. J. 81 1-25
29. Shilnikov L P 1967 On a Poincaré-Birkhoff problem Math. USSR Sb. 74
30. Marsden J 1968 Generalized Hamiltonian mechanics; a mathematical exposition of non-smooth dynamical systems and classical Hamiltonian mechanic Arch. Ration. Mech. Anal. 28 323-61
31. Newhouse S 1977 Quasi-elliptic periodic points in conservative dynamical systems Am. J. Math. 99 1061-987
32. Russman H 1970 Kleine nenner I, Uber invariante Kurven differenzierbarer Abbildungen eines Kreisrings Nachr. Akad. Wiss. Goett., Math. Phys. Kl. II 67-105
33. Sinai Y 1963 On the foundations of the ergodic hypothesis for dynamical system of statistical mechanics Dokl. Akad. Nauk SSSR 153 1261-4
34. Sinai Y 1970 Dynamical systems with elastic reflections: Ergodic properties of scattering billiards Russ. Math. Surv. 25 137-89
35. Sinai Y and Chernov N 1987 Ergodic properties of some systems of two-dimensional disks and three-dimensional balls Usp. Mat. Nauk 42 153-74
36. Sinai Y and Chernov N 1987 Ergodic properties of some systems of two-dimensional disks and three-dimensional balls Usp. Mat. Nauk 42 256
37. Smale S 1963 Diffeomorphisms with many periodic points Differential and Combinatorial Topology ed C Cairns (Princeton, NJ: Princeton Univeristy Press) pp 63-80
38. Smilansky U 1995 Semiclassical quantization of chaotic billiards - a scattering approach Proc. 1994 Les-Houches Summer School on 'Mesoscopic Quantum Physics' ed A Akkermans et al
39. Szász 1996 Boltzmann's ergodic hypothesis, a conjecture for centuries? Stud. Sci. Math. Hung. 31 299-322
40. Wojtkowski M 1986 Principles for the design of billiards with nonvanishing Lyapunov exponents Commun. Math. Phys. 105 391-414