Relative volume of Kolmogorov-Arnold-Moser tori and uniform distribution, stickiness and nonstickiness in Hamiltonian systems

Nonlinearity

Volumn 21, Issue 2, 2008, Pages

  Bunimovich, Leonid A ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43049135867     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/2/T01     Document Type: Article

References (18)

1. Altmann E G, Motter A E and Kantz H 2005 Stickiness in mushroom billiards Chaos 15 033105
2. Altmann E G, Motter A E and Kantz H 2006 Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space Phys. Rev. E 73 026207
3. Bunimovich L A 1988 Two mechanisms of dynamical chaos: permanent stochasticity and intermittency Nonlinear and Turbulent Process in Physics ed V G Bar'yakhter et al (Kiev: Naukova Dumka) pp 190-3
4. Bunimovich L A 2001 Mushrooms and other billiards with divided phase space Chaos 11 802-8
5. Bunimovich L A 2003 Kinematics, equilibrium and shape in Hamiltonian systems Chaos 13 903-12
6. Bunimovich L A and Del Magno G 2006 Semi-focusing billiards: hyperbolicity Commun. Math. Phys. 262 17-32
7. Chernov N I 1999 Decay of correlations and dispersing billiards J. Stat. Phys. 94 513-56
8. Chirikov B V and Shepelyansky D L 1984 Correlation properties of dynamical chaos in Hamiltonian systems Physica D 13 395-414
9. Donnay V J 1988 Geodesic flow on the two-sphere I. Positive measure entropy Ergod. Theory Dynam. Syst. 8 531-53
10. Liverani C 2004 Birth of an elliptic island in a chaotic sea Math. Phys. Electron. J. 10 13pp
11. Markus L and Meyer K R 1978 Generic Hamiltonian dynamical systems are neither integrable nor ergodic Mem. Am. Math. Soc. 144 1-52
12. Morbidelli A and Giorgilli A 1995 Superexponential stability of KAM tori J. Stat. Phys. 78 1607-17
13. Perry A and Wiggins S 1994 KAM tori are very sticky: rigorous lower bounds on the time to move away from an invariant Lagrangian torus with linear flow Physica D 71 102-21
14. Porter M and Lansel S 2006 Mushroom billiards AMS Notices 53 334-7
15. Przytycki F 1982 Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behavior Ergod. Theory Dynam. Syst. 2 439-63
16. Wojtkowski M 1981 A model problem with the coexistence of stochastic and integrable behavior Commun. Math. Phys. 80 453-64
17. Wojtkowski M 1982 On the ergodic properties of piecewise linear perturbations of the twist map Ergod. Theory Dynam. Syst. 2 525-42
18. Zaslavsky G M 2002 Chaos, fractional kinetics and anomalous transport Phys. Rep. 371 461-580