Prog. Theor. Phys. Vol. 78 No. 4 (1987) pp. 721-726

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Letters

Spectra of Singularities for the Lozi and Hénon Maps

Hiroki Hata, Terumitsu Morita, Koji Tomita and Hazime Mori

Department of Physics, Kyushu University 33, Fukuoka 812

(Received May 6, 1987)

Abstract:

The spectra of singularities as well as the generalized dimensions and entropies are explicitly derived for the strange attractors of the two-dimensional Lozi map and Hénon map from the dynamical viewpoints with the aid of relations obtained in a previous paper.

URL : http://ptp.ipap.jp/link?PTP/78/721/
DOI : 10.1143/PTP.78.721

References:

T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A33 (1986),1141[APS].
T. Morita, H. Hata, H. Mori, T. Horita and K. Tomita, Prog. Theor. Phys. 78 (1987), 511[PTP].
P. Grassberger, Phys. Lett. 107A (1985), 101.
M. Sano, S. Sato and Y. Sawada, Prog. Theor. Phys. 76 (1986), 945[PTP].
J. -P. Eckmann and I. Procaccia, Phys. Rev. A34 (1986), 659[APS].
R. Lozi, J. de Phys. 39 (1978), 9.
M. Hénon, Commun. Math. Phys. 50 (1976), 69[CrossRef].
P. Grassberger, Phys. Lett. 97A (1983), 224.
We carried out this calculation by using the results by C. Simo, J. Stat. Phys. 21 (1979), 465.

Citing Article(s) :

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Spectra of Singularities and Entropies for Local Expansion Rates

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Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 923-928 :
Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in Two-Dimensional Maps

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Progress of Theoretical Physics Vol. 121 No. 6 (2009) pp. 1143-1156 :
Time Correlation Calculation Method Based on Delayed Coordinates

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