Prog. Theor. Phys. Vol. 76 No. 4 (1986) pp. 945-948

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Letters

Global Spectral Characterization of Chaotic Dynamics

Masaki Sano, Shinichi Sato and Yasuji Sawada

Research Institute of Electrical Communication, Tohoku University, Sendai 980

(Received June 27, 1986)

Abstract:

We propose a new global characterization of chaotic dynamics. It gives a unified description of some aspects of chaos (e.g., the relationships among dimensions of invariant measures, Lyapunov exponents, and entropies; strange attractor vs repeller; and the variational principle). We apply this formalism to a few examples employing a practical algorithm.

URL : http://ptp.ipap.jp/link?PTP/76/945/
DOI : 10.1143/PTP.76.945

References:

T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A33 (1986), 1141, [APS]and references therein.
P. Grassberger, Physica 4D (1985), 365[Elsevier].
Our results has a close relation to the variational formalism: Y. Takahashi and Y. Oono, Prog. Theor. Phys. 71 (1984), 851, [PTP]and references therein.
H. Kantz and P. Grassberger, Physica 17D (1985), 75[Elsevier].
J. A. Yorke and E. D. Yorke, J. Stat. Phys. 21 (1979), 263.
P. Grassberger and I. Procaccia, Phys. Rev. A28 (1983), 2591[APS].
H. Fujisaka, Prog. Theor. Phys. 70 (1983), 1264[PTP].
S. Takesue and K. Kaneko, Prog. Theor. Phys. 71 (1984), 35[PTP].
J. P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57 (1983), 1617[APS].
P. Collet, J. P. Crutchfield and J. P. Eckmann, Commun. Math. Phys. 88 (1983), 257[CrossRef].
M. Sano, S. Sato and Y. Sawada, to be published.

Citing Article(s) :

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q-Phase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points

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