Poincaré recurrences in Hamiltonian systems with a few degrees of freedom

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Shepelyansky, D L ^a  

^a UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC DECAY; AVERAGE VALUES; DEGREES OF FREEDOM; HAMILTONIAN SYSTEMS; NUMBER OF DEGREES OF FREEDOM; NUMERICAL SIMULATION; PHASE SPACES; POINCARE; POWER LAW; STABILITY ISLANDS; SYMPLECTIC MAP;

MECHANICS; PHASE SPACE METHODS;

HAMILTONIANS;

EID: 78651377857     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.055202     Document Type: Article

References (25)

1. H. Poincaré, Acta Math. 13, 1 (1890).
2. J. Barrow-Green, History of Mathematics (American Mathematical Society/London Mathematical Society, Providence, RI, 1997), Vol. 11.
3. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, Paris, 1968).
4. I. P. Cornfeld, S. V. Fomin, and Y. G. Sinai, Ergodic Theory (Springer, New York, 1982).
5. B. V. Chirikov, Phys. Rep. 52, 263 (1979). 10.1016/0370-1573(79)90023-1
6. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer, Berlin, 1992).
7. B. V. Chirikov and D. L. Shepelyansky, Proceedings of the Ninth International Conference on Nonlinear Oscillations (Kiev, 1981), Naukova Dumka 2, 420 (1984)
8. Princeton University Report No. PPPL-TRANS-133, 1983.
9. C. F. F. Karney, Physica D 8, 360 (1983). 10.1016/0167-2789(83)90232-4
10. B. V. Chirikov and D. L. Shepelyansky, Physica D 13, 395 (1984). 10.1016/0167-2789(84)90140-4
11. J. D. Meiss and E. Ott, Phys. Rev. Lett. 55, 2741 (1985) 10.1103/PhysRevLett.55.2741
12. J. D. Meiss and E. Ott, Physica D 20, 387 (1986). 10.1016/0167-2789(86) 90041-2
13. B. V. Chirikov and D. L. Shepelyansky, Phys. Rev. Lett. 82, 528 (1999) 10.1103/PhysRevLett.82.528
14. B. V. Chirikov and D. L. Shepelyansky, Phys. Rev. Lett. 89, 239402 (2002). 10.1103/PhysRevLett.89.239402
15. G. Cristadoro and R. Ketzmerick, Phys. Rev. Lett. 100, 184101 (2008). 10.1103/PhysRevLett.100.184101
16. R. Artuso and C. Manchein, Phys. Rev. E 80, 036210 (2009). 10.1103/PhysRevE.80.036210
17. M. Ding, T. Bountis, and E. Ott, Phys. Lett. A 151, 395 (1990). 10.1016/0375-9601(90)90910-G
18. E. G. Altmann and H. Kantz, EPL 78, 10008 (2007). 10.1209/0295-5075/78/ 10008
19. K. Kaneko and T. Konishi, Phys. Rev. A 40, 6130 (1989) 10.1103/PhysRevA.40.6130
20. K. Kaneko and T. Konishi, J. Phys. A: Math. Gen. 23, L715 (1990). 10.1088/0305-4470/23/15/004
21. B. V. Chirikov and V. V. Vecheslavov, J. Stat. Phys. 71, 243 (1993). 10.1007/BF01048098
22. B. V. Chirikov and V. V. Vecheslavov, Sov. Phys. JETP 85, 616 (1997) 10.1134/1.558346
23. [B. V. Chirikov and V. V. Vecheslavov, Zh. Eksp. Teor. Fiz. 112, 1132 (1997)].
24. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001). 10.1017/CBO9780511606014
25. D. E. Shaw, P. Maragakis, K. Lindorff-Larsen, S. Piana, R. O. Dror, M. P. Eastwood, J. A. Bank, J. M. Jumper, J. K. Salmon, Y. Shan, and W. Wriggers, Science 330, 341 (2010). 10.1126/science.1187409