Torus fractalization and intermittency

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 6, 2002, Pages

  Kuznetsov, Sergey P ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; DATA ACQUISITION; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS;

INTERMITTENCY; RENORMALIZATION GROUP (RG); STRANGE NONCHAOTIC ATTRACTOR (SNA); TORUS FRACTALIZATION (TF);

BIFURCATION (MATHEMATICS);

EID: 42749108729     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.066209     Document Type: Article

References (32)

1. L. D. Landau, C. R. (Dokl.) Acad. Sci. URSS 44, 311 (1944).
2. E. Hopf, Commun. Pure Appl. Math. 1, 303 (1948).
3. D. Ruelle and F. Takens, Commun. Math. Phys. 20, 167 (1971).
4. C. Grebogi, E. Ott, S. Pelikan, and J. A. Yorke, Physica D 13, 261 (1984).
5. F. J. Romeiras, A. Bondeson, E. Ott, T. M. Antonsen, and C. Grebogi, Physica D 26, 277 (1987).
6. A. S. Pikovsky and U. Feudel, Chaos 5, 253 (1995).
7. M. J. Feigenbaum, J. Stat. Phys. 19, 25 (1978).
8. M. J. Feigenbaum, J. Stat. Phys. 21, 669 (1979).
9. E. B. Vul, Y. G. Sinai, and K. M. Khanin, Russ. Math. Surveys 39, 1(1984).
10. D. Rand, S. Ostlund, J. Sethna, and E. D. Siggia, Phys. Rev. Lett. 49, 132 (1982).
11. S. Ostlund, D. Rand, J. Sethna, and E. D. Siggia, Physica D 8, 303 (1983).
12. M. J. Feigenbaum, L. P. Kadanoff, and S. J. Shenker, Physica D 5, 370 (1982).
13. A. P. Kuznetsov, S. P. Kuznetsov, and I. R. Sataev, Physica D 109, 91 (1997).
14. S. P. Kuznetsov, A. S. Pikovsky, and U. Feudel, Phys. Rev. E 51, R1629 (1995).
15. S. Kuznetsov, U. Feudel, and A. Pikovsky, Phys. Rev. E 57, 1585 (1998).
16. S. P. Kuznetsov, E. Neumann, A. Pikovsky, and I. R. Sataev, Phys. Rev. E 62, 1995 (2000).
17. Y. Pomeau and P. Manneville, Commun. Math. Phys. 74, 189 (1980).
18. B. Hu and J. Rudnick, Phys. Rev. Lett. 48, 1645 (1982).
19. J. E. Hirsch, B. A. Huberman, and D. J. Scalapino, Phys. Rev. A 25, 519 (1982).
20. F. Argoul and A. Arneodo, J. Phys. (France) 46, L901 (1985);
21. H. Daido, Prog. Theor. Phys. 71, 402 (1984).
22. U. Feudel, A. S. Pikovsky, and J. Kurths, Physica D 88, 176 (1995).
23. P. G. Harper, Proc. Phys. Soc., London, Sect. A 68, 854 (1955).
24. I. M. Suslov, Zh. Eksp. Teor. Fiz. 83, 1079 (1982).
25. S. Ostlund and R. Pandit, Phys. Rev. B 29, 1394 (1984).
26. J. A. Ketoja and I. I. Satija, Physica D 109, 70 (1997).
27. B. D. Mestel, A. H. Osbaldestin, and B. Winn, J. Math. Phys. 41, 8304 (2000).
28. S. S. Negi and R. Ramaswamy, Phys. Rev. E 64, 045204 (2001).
29. H. Osinga, J. Wiersig, P. Glendinning, and U. Feudel, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 3085 (2001).
30. S. Aubry and G. Andre, in Proceedings of the Israel Physical Society, edited by C. G.Kuper (Hilger, Bristol, 1979), Vol. 3, p. 133.
31. A. P. Kuznetsov, S. P. Kuznetsov, and I. R. Sataev, Phys. Lett. A 189, 367 (1994).
32. N. Y. Ivankov and S. P. Kuznetsov, Phys. Rev. E 63, 046210 (2001).