Analytic Study of Periodic Chaos : Method and Spectral Characteristics : Condensed Matter and Statistical Physics)

概要

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An analytic method of calculating the time-correlation function of nonperiodic orbits is developed for periodic chaos generated by continuous one-dimensional maps with a single maximum. It is based on the ergodicity and its formulated as an eigenvalue problem of the Frobenius-Perron operator. The correlation function consists of two parts, one is periodic and the other chaotic, and the final formulas state that both parts are obtained if we only know a finite sequence of points on the orbit passing through the position at which the mapping function is maximum. The present method, though rigorous for the tent map, includes generally certain approximations, which become increasingly good as the chaotic critical point is approached. The explicit results at the band-splitting points of the logistic map, together with the power spectra, are in excellent agreement with numerical experiments. Characteristic features of the power spectra are discussed and an intrinsic relation between the intensities of the periodic and chaotic spectra is pointed out.
一般社団法人日本物理学会の論文
1984-11-25