Scale-local dimensions of strange attractors

Abstract

We compare limit-based and scale-local dimensions of complex distributions, particularly for a strange attractor of the Henon map. Scale-local dimensions as distributions on scale are seen to exhibit a wealth of detail. Limit-based dimensions are shown to be averages of scale-local dimensions, in principle over a semi-infinite scale interval. We identify some critical questions of definition for practical dimension analysis of arbitrary distributions on bounded scale intervals.