Arnold diffusion in large systems

Journal of Experimental and Theoretical Physics

Volumn 85, Issue 3, 1997, Pages 616-624

  Chirikov, B V ^a   Vecheslavov, V V ^a  

^a BUDKER INSTITUTE OF NUCLEAR PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644930421     PISSN: 10637761     EISSN: None     Source Type: Journal    
DOI: 10.1134/1.558346     Document Type: Article

References (50)

1. B. V. Chirikov, Phys. Rep. 52, 263 (1979).
2. A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, Springer (1992).
3. V. I. Arnold, Dokl. Akad. Nauk SSSR 156, 9 (1964).
4. B. V. Chirikov, Studies in the Theory of Nonlinear Resonance and Stochasticity, preprint INP-267, Novosibirsk (1969)
5. (Engl. trans., CERN Trans. 71-40, 1971).
6. G. V. Gadiyak, F. M. Izrailev, and B. V. Chirikov, Proc. 7th Intern. Conf. on Nonlinear Oscillations, Akademie-Verlag, Berlin (1977), Vol. II, 1. p. 315.
7. J. Tennyson, M. Lieberman, and A. Lichtenberg, AIP Conf. Proc. 57, 272 (1979);
8. M. Lieberman, Ann. N.Y. Acad. Sci. 357, 119 (1980).
9. B. V. Chirikov, J. Ford, and F. Vivaldi, AIP Conf. Proc. 57, 323 (1979).
10. T. Petrosky, Phys. Rev. A 29, 2078 (1984).
11. B. Wood, A. Lichtenberg, and M. Lieberman, Physica D 71, 132 (1994).
12. N. N. Nekhoroshev, Usp. Mat. Nauk 32, (6), 5 (1977).
13. P. Lochak, Phys. Lett. A 143, 39 (1990);
14. Usp. Mat. Nauk 47, (6), 59 (1992);
15. P. Lochak and A. Neishtadt, Chaos 2, 495 (1992).
16. A. A. Chernikov, R. Z. Sagdeev, and G. M. Zaslavsky, Physica D 33, 65 (1988);
17. A. Lichtenberg and B. Wood, Phys. Rev. A 39, 2153 (1989);
18. B. V. Chirikov and V. V. Vecheslavov, in From Phase Transitions to Chaos, ed. by G. Györgyi et al. World Scientific (1992), p. 273.
19. N. N. Filonenko, R. Z. Sagdeev, and G. M. Zaslavsky, Nucl. Fusion 7, 253 (1967);
20. G. M. Zaslavsky and N. N. Filonenko, Zh. Eksp. Teor. Fiz. 54, 1590 (1968);
21. G. M. Zaslavsky and B. V. Chirikov, Usp. Fiz. Nauk 105, 3 (1971);
22. A. Rechester and T. Stix, Phys. Rev. Lett. 36, 587 (1976);
23. D. Escande, Phys. Rep. 121, 163 (1985);
24. V. F. Lazutkin, Dokl. Akad. Nauk SSSR 313, 268 (1990);
25. V. V. Afanasiev et al., Phys. Lett. A 144, 229 (1990).
26. B. V. Chirikov and V. V. Vecheslavov, How Fast is Arnold Diffusion? Preprint INP 89-72, Novosibirsk (1989).
27. B. V. Chirikov and V. V. Vecheslavov, in Analysis etc. ed. by P. Rabinowitz and E. Zehnder, Academic Press (1990), p. 219.
28. B. V. Chirikov, Fiz. Plasmy 4, 521 (1978);
29. Proc. R. Soc. London, Ser. A 413, 145 (1987).
30. K. Kaneko and T. Konishi, Phys. Rev. A 40, 6130 (1989);
31. T. Konishi, Prog. Theor. Phys. Suppl. 98, 19 (1989);
32. T. Konishi and K. Kaneko, J. Phys. A 23, L715 (1990).
33. B. V. Chirikov and V. V. Vecheslavov, J. Stat. Phys. 71, 243 (1993).
34. Resonances in the Motion of Planets, Satellites and Asteroids, ed. by S. Ferraz-Mello and W. Sessin, Univ. de Sao Paulo, Brazil (1985);
35. J. Wisdom, Icarus 72, 241 (1987);
36. J. Laskar, Nature (London) 338, 237 (1989);
37. Icarus 88, 266 (1990);
38. Astron. Astrophys. 287, L9 (1994).
39. B. V. Chirikov, Priroda 7, 15 (1982);
40. Nolinear Dynamics Aspects of Particle Accelerators, Lecture Notes in Physics, Vol. 247, Springer (1986);
41. A. Lichtenberg, Phys. Fluids B 4, 3132 (1992).
42. V. F. Lazutkin et al., Physica D 40, 235 (1989).
43. V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 109, 2208 (1996)
44. [JETP 82, 1190 (1996)].
45. A. Ya. Khinchin, Continued fractions, Fizmatgiz, Moskva (1961) (in Russian);
46. J. Cassels, An Introduction to Diophanline Approximation, Cambridge University Press (1957);
47. W. Schmidt, Diophantine Approximations, Lecture Notes in Mathematics 785, Springer (1980).
48. B. V. Chirikov, Chaos, Solitons and Fractals 1, 79 (1991).
49. E. Wayne, Commun. Math. Phys. 104, 21 (1986).
50. J. von Milczewski, G. Diercksen, and T. Uzer, Phys. Rev. Lett. 76, 2890 (1996).