English

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.

Keywords

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

R2 v1 2026-07-22T16:22:52.137Z