Prog. Theor. Phys. Vol. 85 No. 2 (1991) pp. 187-204

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New Asymptotic Law Governing Overall Temporal Correlations in Chaotic Systems

— Ensemble Homogenization and Order-q Power Spectrum —

Hirokazu Fujisaka and Hiroshi Shibata

Department of Physics, Kyushu University 33, Fukuoka 812

(Received August 22, 1990)

Abstract:

A new statistical-physical asymptotic law relevant to explicit correlation in temporal fluctuations generated by chaotic dynamics is found. Homogenizing the ensemble members, we can introduce the order-q power spectrum I_q(ω) in the “thermodynamic” limit, whose poles are proved to be determined by the eigenvalues of the order-q evolution operator H_q previously introduced. It is a natural extension of the conventional power spectrum I(ω)(= I_q=0(ω)), and enables us to study various correlation characteristics by controlling the value of parameter q. This manifests that the intensive variable q governs overall temporal-correlation characteristics as well as the global aspect described by fluctuation-spectrum theory.

URL : http://ptp.ipap.jp/link?PTP/85/187/
DOI : 10.1143/PTP.85.187

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