Generalized dimensions of strange attractors
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 are the capacity, the information dimension, and the correlation exponent, respectively. For all q, they are measurable from recurrence times in a time series, without need for a boxcounting algorithm. For the Feigenbaum map and for the generalized Baker transformation, all generalized dimensions are finite and calculable, and depend nontrivially on q.
 Publication:

Physics Letters A
 Pub Date:
 September 1983
 DOI:
 10.1016/03759601(83)907533
 Bibcode:
 1983PhLA...97..227G
 Keywords:

 Strange Attractors;
 Theoretical Physics;
 Dimensions;
 Entropy;
 Maps;
 Time Series Analysis;
 Physics (General)