Prog. Theor. Phys. Vol. 77 No. 2 (1987) pp. 239-253

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Characteristic Structures of Power Spectra in Periodic Chaos. II

— The Hénon Map, the Driven Damped Pendulum and the Rössler System —

Takeshi Yoshida and Koji Tomita

Department of Physics, Kyushu University 33, Fukuoka 812

(Received September 16, 1986)

Abstract:

The recursion relations for the power spectra of periodic chaos derived for one-dimensional maps in a previous paper are applied to periodic chaos in higher dimensional systems. Specifically, the Hénon map, the driven damped pendulum and the Rössler system are considered, and Poincaré maps are taken for the latter two systems. In testing the recursion relations, power spectra are computed numerically for these maps, and it is shown that near the chaotic critical point both the components of these two-dimensional maps have spectral structures which are governed by the same recursion relations. It is also shown that these relations hold independently of the location of the cross sections on which the Poincaré maps are defined. The universal applicability of the recursion relations is asserted near the critical point.

URL : http://ptp.ipap.jp/link?PTP/77/239/
DOI : 10.1143/PTP.77.239

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Citing Article(s) :

Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63 :
Statistical Mechanics of Dynamical Systems

Hazime Mori, Hiroki Hata, Takehiko Horita and Tatsuharu Kobayashi