Prog. Theor. Phys. Vol. 63 No. 3 (1980) pp. 1044-1047

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Letters

Fractal Dimensions of Chaotic Flows of Autonomous Dissipative Systems

Hazime Mori

Department of Physics, Kyushu University, Fukuoka 812

(Received December 13, 1979)

Abstract:

The fractal dimensions of chaotic flows are shown to be given D=m⁰+m⁺{1+|λ⁺/λ^-|}, where m⁰ and m⁺ are the numbers of zero and positive Lyapunov characteristic exponents λ_α and λ^± are the mean values of positive and negative λ_α respectively.

URL : http://ptp.ipap.jp/link?PTP/63/1044/
DOI : 10.1143/PTP.63.1044

References:

B. B. Mandelbrot, Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977); in Turbulence Seminar, Lecture Notes in Math. vol. 615, eds. A. Dold and B. Eckmann (Springer, 1977) and references cited therein.
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D. Ruelle, Statistical Mechanics and Dynamical Systems, Duke Univ. Math. Series III (Math. Dept., Duke Univ., Durham, U. S. A., 1977).
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Progress of Theoretical Physics Vol. 87 No. 5 (1992) pp. 1107-1118 :
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