Generalized dimensions of strange attractors
DOI: 10.1016/0375-9601(83)90753-3
关键词: Attractor 、 Exponent 、 Monotonic function 、 Information dimension 、 Entropy (information theory) 、 Time series 、 Physics 、 Pure mathematics
摘要: Abstract It is pointed out that there exists an infinity of generalized dimensions for strange attractors, related to the order-q Renyi entropies. They are monotonically decreasing with q. For q = 0, 1 and 2, they capacity, information dimension, correlation exponent, respectively. all q, measurable from recurrence times in a time series, without need box-counting algorithm. Feigenbaum map Baker transformation, finite calculable, depend non-trivially on
harvard.edu
elsevier.com
sci-hub.se 参考文章(9)
David A. Russell, James D. Hanson, Edward Ott, Dimension of Strange Attractors Physical Review Letters. ,vol. 45, pp. 1175- 1178 ,(1980) , 10.1103/PHYSREVLETT.45.1175
M. Mackey, L Glass, Oscillation and chaos in physiological control systems Science. ,vol. 197, pp. 287- 289 ,(1977) , 10.1126/SCIENCE.267326
M. Hénon, A Two-dimensional Mapping with a Strange Attractor Communications in Mathematical Physics. ,vol. 50, pp. 69- 77 ,(1976) , 10.1007/BF01608556
Mitchell J. Feigenbaum, The universal metric properties of nonlinear transformations Journal of Statistical Physics. ,vol. 21, pp. 669- 706 ,(1979) , 10.1007/BF01107909
J.Doyne Farmer, Edward Ott, James A. Yorke, The dimension of chaotic attractors Physica D: Nonlinear Phenomena. ,vol. 7, pp. 153- 180 ,(1983) , 10.1016/0167-2789(83)90125-2
Mitchell J. Feigenbaum, Quantitative universality for a class of nonlinear transformations Journal of Statistical Physics. ,vol. 19, pp. 25- 52 ,(1978) , 10.1007/BF01020332
H. S. Greenside, A. Wolf, J. Swift, T. Pignataro, Impracticality of a box-counting algorithm for calculating the dimensionality of strange attractors Physical Review A. ,vol. 25, pp. 3453- 3456 ,(1982) , 10.1103/PHYSREVA.25.3453
P. Grassberger, On the fractal dimension of the Henon attractor Physics Letters A. ,vol. 97, pp. 224- 226 ,(1983) , 10.1016/0375-9601(83)90752-1
H.G.E. Hentschel, Itamar Procaccia, The infinite number of generalized dimensions of fractals and strange attractors Physica D: Nonlinear Phenomena. ,vol. 8, pp. 435- 444 ,(1983) , 10.1016/0167-2789(83)90235-X