Scale-local dimensions of strange attractors
Mathematical Physics
2007-05-23 v1 math.MP
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.
Cite
@article{arxiv.math-ph/0305022,
title = {Scale-local dimensions of strange attractors},
author = {J. G. Reid and T. A. Trainor},
journal= {arXiv preprint arXiv:math-ph/0305022},
year = {2007}
}
Comments
12 pages, 5 figures