Complex periodic orbits, renormalization, and scaling for quasiperiodic golden-mean transition to chaos

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

Volumn 63, Issue 4, 2001, Pages

  Ivankov, N Y ^a   Kuznetsov, S P ^b  

^a SARATOV STATE UNIVERSITY   (Russian Federation)

^b INSTITUTE OF RADIO ENGINEERING AND ELECTRONICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; MATRIX ALGEBRA; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS;

FIBONACCI NUMBER; RENORMALIZATION GROUP (RG);

CHAOS THEORY;

EID: 0035306226     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.046210     Document Type: Article

References (39)

1. L.D. Landau, Dokl. Akad. Nauk SSSR 44, 339 (1944).
2. D. Ruelle and F. Takens, Commun. Math. Phys. 20, 167 (1971).
3. S.J. Shenker, Physica D 5, 405 (1982).
4. M.J. Feigenbaum, L.P. Kadanoff, and S.J. Shenker, Physica D 5, 370 (1982).
5. D. Rand, S. Ostlund, J. Sethna, and E.D. Siggia, Phys. Rev. Lett. 49, 132 (1982).
6. D. Rand, S. Ostlund, J. Sethna, and E.D. Siggia, Physica D 8, 303 (1983).
7. M.H. Jensen, M.H. Bak, and T. Bohr, Phys. Rev. Lett. 50, 1637 (1983).
8. M.H. Jensen, M.H. Bak, and T. Bohr, Phys. Rev. A 30, 1960 (1984).
9. M.H. Jensen, M.H. Bak, and T. Bohr, Phys. Rev. A 30, 1970 (1984).
10. C. Grebogi, E. Ott, S. Pelikan, and J.A. Yorke, Physica D 13, 261 (1984).
11. K. Kaneko, Prog. Theor. Phys. 71, 282 (1984).
12. J.D. Farmer and I.I. Satija, Phys. Rev. A 31, 3520 (1985).
13. M.H. Jensen, L.P. Kadanoff, A. Libchaber, I. Procaccia, and J. Stavans, Phys. Rev. Lett. 55, 2798 (1985).
14. J. Stavans, F. Helsot, and A. Libchaber, Phys. Rev. Lett. 55, 596 (1985).
15. C. Grebogi, E. Ott, and J.A. Yorke, Physica D 15, 354 (1985).
16. R.E. Ecke, J.D. Farmer, and D.K. Umberger, Nonlinearity 2, 175 (1989).
17. X.-W. Wang, R. Mainieri, and J. Hlowenstein, Phys. Rev. A 40, 5382 (1989).
18. S. Kim, R.S. MacKay, and J. Guckenheimer, Nonlinearity 2, 391 (1989).
19. B. Fourcade and A.-M.S. Tremblay, J. Stat. Phys. 61, 607 (1990).
20. B. Fourcade and A.-M.S. Tremblay, J. Stat. Phys. 61, 639 (1990).
21. Guckenheimer J. Baesens, S. Kim, and R.S. MacKay, Physica D 49, 387 (1991).
22. D. Rockmore, R. Siegel, N. Tongring, and C. Tresser, Chaos 1, 25 (1991).
23. S.-Y. Kim and B. Hu, Phys. Rev. A 44, 934 (1991).
24. S.-Y. Kim, and D.-S. Lee, Phys. Rev. A 45, 5480 (1992).
25. J.A. Ketoja, Phys. Rev. Lett. 69, 2180 (1992).
26. V.W. Spinadel, Chaos, Solitons Fractals 8, 1631 (1992).
27. V. Baladi, D. Rockmore, N. Tongring, and C. Tresser, Nonlinearity 5, 1111 (1992).
28. T.W. Dixon, T. Gherghetta, and B.G. Kenny, Chaos 6, 32 (1996).
29. T.W. Dixon and B.G. Kenny, J. Math. Phys. 39, 5952 (1998).
30. M.J. Feigenbaum, J. Stat. Phys. 21, 669 (1979).
31. B. Derrida, A. Gervois, and Y. Pomeau, J. Phys. A 12, 269 (1979).
32. B. Hu and J.-M. Mao, Phys. Lett. 108A, 305 (1985).
33. A.P. Kuznetsov, S.P. Kuznetsov, and I.R. Sataev, Physica D 109, 91 (1997).
34. J.S. Bastos de Figueiredo and C.P. Malta, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 281 (1998).
35. A. J. Lichtenberg and M. A. Lieberman (unpublished).
36. S.J. Shenker and L.P. Kadanoff, J. Stat. Phys. 27, 631 (1982).
37. L.P. Kadanoff, Phys. Rev. Lett. 47, 1641 (1981).
38. R.S. MacKay, Physica D 7, 283 (1983).
39. T.S. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman, Phys. Rev. A 33, 1141 (1986).