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Scale-local dimensions of strange attractors

J. G. Reid·T. A. Trainor
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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.

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J. G. Reid, T. A. Trainor. 2003-05-09. Scale-local dimensions of strange attractors. https://arxiv.org/abs/math-ph/0305022

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