论文信息 - The fractal dimension of the Lorenz attractor - 字舞流文

The fractal dimension of the Lorenz attractor

Abstract Taken's box-counting algorithm for computing the fractal dimension of a strange attractor is applied to the Lorenz equation. A convergence problem is discussed, and an approximate dimension is computed.

Mark J. McGuinness | M. McGuinness | M. Mcguinness

[1] E. Ott,et al. Dimension of Strange Attractors , 1980 .

[2] James A. Yorke,et al. Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model , 1979 .

[3] R. Graham,et al. Probability density of the Lorenz model , 1983 .

[4] J. D. Farmer,et al. Order within chaos , 1984 .

[5] A. Wolf,et al. Impracticality of a box-counting algorithm for calculating the dimensionality of strange attractors , 1982 .

[6] Abraham Boyarsky,et al. On a class of transformations which have unique absolutely continuous invariant measures , 1979 .

[7] J. Yorke,et al. Period Three Implies Chaos , 1975 .

[8] E. Lorenz. Deterministic nonperiodic flow , 1963 .

[9] H. Peitgen,et al. Functional Differential Equations and Approximation of Fixed Points , 1979 .

[10] J. Yorke,et al. On the existence of invariant measures for piecewise monotonic transformations , 1973 .

[11] F. Takens. Detecting strange attractors in turbulence , 1981 .

[12] Hazime Mori,et al. Fractal Dimensions of Chaotic Flows of Autonomous Dissipative Systems , 1980 .

[13] B. Mandelbrot,et al. Fractals: Form, Chance and Dimension , 1978 .

[14] I. Shimada,et al. A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems , 1979 .