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Prog. Theor. Phys. Vol. 91 No. 4 (1994) pp. 677-692

[ Full Text PDF : FREE ACCESS (1523K) ]

On the Linear Slopes in the Expansion-Rate Spectra of Chaos

Takehiko Horita and Hazime Mori*

Department of Control Engineering and Science, Kyushu Institute of Technology, Iizuka 820
*Department of Physics, Kyushu Kyoritsu University, Kitakyushu 807

(Received August 18, 1993)

Abstract:

Linear slopes in the expansion-rate spectra of chaos due to nonhyperbolicity are formulated in order to characterize the geometric structures of chaos in phase space from the statistical point of view. Tangency points of the stable and unstable manifold bring about a linear slope sα = -1 in the expansion-rate spectra. A singular structure due to the accumulation of homoclinic or heteroclinic tangency points at the crisis point brings about a linear slope sβ in the expansion-rate spectra, which is theoretically formulated in terms of the eigenvalues of certain poriodic orbit collided with the attractor. Similar linear slopes also appear in the singularity spectra f(α) of chaos, which are related to the above linear slopes sα and sβ.


URL : http://ptp.ipap.jp/link?PTP/91/677/
DOI : 10.1143/PTP.91.677

[ Full Text PDF : FREE ACCESS (1523K) ] Citation:

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