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Prog. Theor. Phys. Supplement No.99 (1989) pp. 64-81

[ Full Text PDF : FREE ACCESS (1873K) ]

Global Bifurcations and Fluctuation Spectra of Local Expansion Rates in Nonlinear Dynamical Systems

Takeshi Yoshida and Syuji Miyazaki

Department of Physics, Kyushu University 33, Fukuoka 812

Abstract:

The definition of the fluctuation spectrum of local expansion rates of nearby orbits is extended to a global region of phase space. It contains information on repellers as well as attractors coexisting in the region. Lyapunov exponents of attractors and repellers, the escape rates for repellers and some structures of these invariant sets are represented by this spectrum. Creations and annihilations of these invariant sets, the change of their nature and interrelations, occurring through global bifurcations when a control parameter value is varied, can be seen clearly in terms of this spectrum. On the basis of the statistical-mechanical formalism for this spectrum some of the invariant sets coexisting in phase space for a fixed value of control parameter are interpreted as in phase equilibrium under the weighted average. At the bifurcation points the present first order phase transitions coincide with those for attractors found in previous papers.


URL : http://ptp.ipap.jp/link?PTPS/99/64/
DOI : 10.1143/PTPS.99.64

[ Full Text PDF : FREE ACCESS (1873K) ] Citation:

References:

  1. H. Fujisaka, Prog. Theor. Phys. 70 (1983), 1264[PTP]; ibid. 71 (1984), 513[PTP].
  2. Y. Takahashi and Y. Oono, Prog. Theor. Phys. 71 (1984), 851[PTP].
  3. J.-P. Eckmann and I. Procaccia, Phys. Rev. A 34 (1986), 659[APS].
  4. M. Sano, S. Sato and Y. Sawada, Prog. Theor. Phys. 76 (1986), 945[PTP].
  5. P. Paladin, L. Peliti and A. Vulpiani, J. of Phys. A 19 (1986), L991[CrossRef].
  6. P. Szépfalusy and T. Tél, Phys. Rev. A 35 (1987), 477[APS].
  7. T. Bohr and D. Rand, Physica D 25 (1987), 387.
  8. H. Fujisaka and M. Inoue, Prog. Theor. Phys. 77 (1987), 1334[PTP].
  9. G. Paladin and A. Vulpiani, Phys. Rep. 156 (1987), 147[CrossRef].
  10. R. Badii and A. Politi, Phys. Rev. A 35 (1987), 1288[APS]; Physica Scripta 35 (1987), 243.
  11. P. Grassberger, R. Badii and A. Politi, J. Stat. Phys. 51 (1988), 135.
  12. T. Morita, H. Hata, H. Mori, T. Horita and K. Tomita, Prog. Theor. Phys. 78 (1987), 511[PTP]; ibid. 79 (1988), 296[PTP].
  13. T. Yoshida and B. C. So, Prog. Theor. Phys. 79 (1988), 1[PTP].
  14. T. Tél, Phys. Rev. A 36 (1987), 2507[APS]; Preprint (1989).
  15. H. Hata, T. Horita, H. Mori, T. Morita and K. Tomita, Prog. Theor. Phys. 80 (1988), 809[PTP].
  16. T. Horita, H. Hata, H. Mori, T. Morita, K. Tomita, S. Kuroki and H. Okamoto, Prog. Theor. Phys. 80 (1988), 793[PTP].
  17. T. Horita, H. Hata, H. Mori, T. Morita and K. Tomita, Prog. Theor. Phys. 80 (1988), 923[PTP].
  18. K. Tomita, H. Hata, T. Horita, H. Mori and T. Morita, Prog. Theor. Phys. 80 (1988), 953[PTP].
  19. K. Tomita, H. Hata, T. Horita, H. Mori and T. Morita, Prog. Theor. Phys. 81 (1989), 1[PTP].
  20. N. Mori, T. Kobayashi, H. Hata, T. Morita, T. Horita and H. Mori, Prog. Theor. Phys. 81 (1989), 60[PTP].
  21. K. Tomita, H. Hata, T. Horita, H. Mori, T. Morita, H. Okamoto and H. Tominaga, Prog. Theor. Phys. 81 (1989), 1124[PTP].
  22. T. Kobayashi, N. Mori, H. Hata, T. Horita, T. Yoshida and H. Mori, Prog. Theor. Phys. 82 (1989), 1[PTP].
  23. T. Yoshida, S. Miyazaki, H. Mori, T. Kobayashi, T. Horita and H. Hata, Prog. Theor. Phys. 82 (1989), 879[PTP].
  24. S. Miyazaki, N. Mori, T. Yoshida, H. Mori, H. Hata and T. Horita, Prog. Theor. Phys. 82 (1989), 863[PTP].
  25. S. Ito, S. Tanaka and H. Nakada, Tokyo J. Math. 2 (1979), 241.
  26. T. Yoshida, H. Mori and H. Shigematsu, J. Stat. Phys. 31 (1983), 279.
  27. H. Fujisaka and M. Inoue, Prog. Theor. Phys. 78 (1987), 268[PTP].
  28. H. Kantz and P. Grassberger, Physica D 17 (1985), 75[CrossRef].
  29. E. N. Lorenz, J. Atoms. Sci. 20 (1963), 130.
  30. J. L. Kaplan and J. A. Yorke, Commun. Math. Phys. 67 (1979), 93[CrossRef].
  31. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Springer-Verlag, New York, 1982).
  32. T. Nagashima and I. Shimada, Prog. Theor. Phys. 58 (1977), 1318[PTP].
  33. J. A. Yorke and E. D. Yorke, J. Stat. Phys. 21 (1979), 263.
  34. H. G. E. Hentschel and I. Procaccia, Physica D 8 (1983), 435[CrossRef].
    P. Grassberger, Phys. Lett. A 97 (1983), 227[CrossRef].
  35. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A 33 (1986), 1141[APS].
  36. E. Ott, W. D. Withers and J. A. Yorke, J. Stat. Phys. 36 (1984), 687.
    D. Katzen and I. Procaccia, Phys. Rev. Lett. 58 (1987), 1169 [APS][ Errata; 58 (1987), 2386[APS]].
  37. P. Szépfalusy, T. Tél, A. Csordás and Z. Kovacs, Phys. Rev. A 36 (1987), 3525[APS].
    X.-J. Wang, Phys. Rev. A 39 (1989), 3214[APS].
  38. T. Bohr and M. H. Jensen, Phys. Rev. A 36 (1987), 4904[APS].
  39. H. Hata, T. Horita, H. Mori, T. Morita and K. Tomita, Prog. Theor. Phys. 81 (1989), 11[PTP].
  40. E. Ott, C. Grebogi and J. A. Yorke, Phys. Lett. A 135 (1989), 343[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 85 No. 2 (1991) pp. 187-204 :
    New Asymptotic Law Governing Overall Temporal Correlations in Chaotic Systems
    Hirokazu Fujisaka and Hiroshi Shibata
  2. Progress of Theoretical Physics Supplement No.161 (2006) pp. 270-273 :
    Crossover between Ballistic and Normal Diffusion
    Syuji Miyazaki

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