Arnold diffusion in large systems

Zhurnal Eksperimental'noj i Teoreticheskoj Fiziki

Volumn 112, Issue 3, 1997, Pages 1132-1146

  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: 0346540701     PISSN: 00444510     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. B. V. Chirikov, Phys. Reports 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) (Engl. trans., CERN Trans, 71-40, 1971).
5. B. V. Chirikov, Studies in the Theory of Nonlinear Resonance and Stochasticity, preprint INP-267, Novosibirsk (1969) (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); M. Lieberman, Ann. N.Y. Acad. Sci. 357, 119 (1980).
8. J. Tennyson, M. Lieberman, and A. Lichtenberg, AIP Conf. Proc. 57, 272 (1979); 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); Usp. Mat. Nauk 47, (6), 59 (1992); P. Lochak and A. Neishtadt, Chaos 2, 495 (1992).
14. P. Lochak, Phys. Lett. A 143, 39 (1990); Usp. Mat. Nauk 47, (6), 59 (1992); P. Lochak and A. Neishtadt, Chaos 2, 495 (1992).
15. P. Lochak, Phys. Lett. A 143, 39 (1990); Usp. Mat. Nauk 47, (6), 59 (1992); 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); A. Lichtenberg and B. Wood, Phys. Rev. A 39, 2153 (1989); B. V. Chirikov and V. V. Vecheslavov, in From Phase Transitions to Chaos, ed. by G. Györgyi et al, World Scientific (1992), p. 273.
17. A. A. Chernikov, R. Z. Sagdeev, and G. M. Zaslavsky, Physica D 33, 65 (1988); A. Lichtenberg and B. Wood, Phys. Rev. A 39, 2153 (1989); B. V. Chirikov and V. V. Vecheslavov, in From Phase Transitions to Chaos, ed. by G. Györgyi et al, World Scientific (1992), p. 273.
18. A. A. Chernikov, R. Z. Sagdeev, and G. M. Zaslavsky, Physica D 33, 65 (1988); A. Lichtenberg and B. Wood, Phys. Rev. A 39, 2153 (1989); 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, Nuclear Fusion 7, 253 (1967); G. M. Zaslavsky and N. N. Filonenko, Zh. Eksp. Teor. Fiz. 54, 1590 (1968);
20. N. N. Filonenko, R. Z. Sagdeev, and G. M. Zaslavsky, Nuclear Fusion 7, 253 (1967); 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. Reports 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), B. V. Chirikov and V. V. Vecheslavov, in Analysis etc, ed. by P. Rabinowitz and E. Zehnder, Academic Press (1990), p. 219.
27. B. V. Chirikov and V. V. Vecheslavov, How Fast is Arnold Diffusion? Preprint INP 89-72, Novosibirsk (1989), 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); Proc. Roy. Soc. Lond. A 413, 145 (1987).
29. B. V. Chirikov, Fiz. Plasmy 4, 521 (1978); Proc. Roy. Soc. Lond. A 413, 145 (1987).
30. K. Kaneko and T. Konishi, Phys. Rev. A 40, 6130 (1989); T. Konishi, Suppl. Prog. Theor. Phys. 98, 19 (1989); T. Konishi and K. Kaneko, J. Phys. A 23, L715 (1990).
31. K. Kaneko and T. Konishi, Phys. Rev. A 40, 6130 (1989); T. Konishi, Suppl. Prog. Theor. Phys. 98, 19 (1989); T. Konishi and K. Kaneko, J. Phys. A 23, L715 (1990).
32. K. Kaneko and T. Konishi, Phys. Rev. A 40, 6130 (1989); T. Konishi, Suppl. Prog. Theor. Phys. 98, 19 (1989); 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); J. Wisdom, Icarus 72, 241 (1987); J. Laskar, Nature 338, 237 (1989); Icarus 88, 266 (1990); Astron. Astrophys. 287, L9 (1994).
35. Resonances in the Motion of Planets, Satellites and Asteroids, ed. by S. Ferraz-Mello and W. Sessin, Univ. de Sao Paulo, Brazil (1985); J. Wisdom, Icarus 72, 241 (1987); J. Laskar, Nature 338, 237 (1989); Icarus 88, 266 (1990); Astron. Astrophys. 287, L9 (1994).
36. Resonances in the Motion of Planets, Satellites and Asteroids, ed. by S. Ferraz-Mello and W. Sessin, Univ. de Sao Paulo, Brazil (1985); J. Wisdom, Icarus 72, 241 (1987); J. Laskar, Nature 338, 237 (1989); Icarus 88, 266 (1990); Astron. Astrophys. 287, L9 (1994).
37. Resonances in the Motion of Planets, Satellites and Asteroids, ed. by S. Ferraz-Mello and W. Sessin, Univ. de Sao Paulo, Brazil (1985); J. Wisdom, Icarus 72, 241 (1987); J. Laskar, Nature 338, 237 (1989); Icarus 88, 266 (1990); Astron. Astrophys. 287, L9 (1994).
38. Resonances in the Motion of Planets, Satellites and Asteroids, ed. by S. Ferraz-Mello and W. Sessin, Univ. de Sao Paulo, Brazil (1985); J. Wisdom, Icarus 72, 241 (1987); J. Laskar, Nature 338, 237 (1989); Icarus 88, 266 (1990); Astron. Astrophys. 287, L9 (1994).
39. B. V. Chirikov, Priroda 7, 15 (1982); Nolinear Dynamics Aspects of Particle Accelerators, Lecture Notes in Physics, Vol. 247, Springer (1986); A. Lichtenberg, Phys. Fluids B 4, 3132 (1992).
40. B. V. Chirikov, Priroda 7, 15 (1982); Nolinear Dynamics Aspects of Particle Accelerators, Lecture Notes in Physics, Vol. 247, Springer (1986); A. Lichtenberg, Phys. Fluids B 4, 3132 (1992).
41. B. V. Chirikov, Priroda 7, 15 (1982); Nolinear Dynamics Aspects of Particle Accelerators, Lecture Notes in Physics, Vol. 247, Springer (1986); A. Lichtenberg, Phys. Fluids B 4, 3132 (1992).
42. V. F. Lazutkin et al., Physica D 40, 235 (1989).
43. V. V. Vecheslavov, Zh. Eksper. Teor. Fiz. 109, 2208 (1996).
44. A. Ya. Khinchin, Continued fractions, Fizmatgiz, Moskva (1961) (in Russian); J. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press (1957); W. Schmidt, Diophantine Approximations, Lecture Notes in Mathematics 785, Springer (1980).
45. A. Ya. Khinchin, Continued fractions, Fizmatgiz, Moskva (1961) (in Russian); J. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press (1957); W. Schmidt, Diophantine Approximations, Lecture Notes in Mathematics 785, Springer (1980).
46. A. Ya. Khinchin, Continued fractions, Fizmatgiz, Moskva (1961) (in Russian); J. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press (1957); W. Schmidt, Diophantine Approximations, Lecture Notes in Mathematics 785, Springer (1980).
47. B. V. Chirikov, Chaos, Solitons and Fractals 1, 79 (1991).
48. E. Wayne, Comm. Math. Phys. 104, 21 (1986).
49. J. von Milczewski, G. Diercksen, and T. Uzer, Phys. Rev. Lett. 76, 2890 (1996).