Lipschitz invariance of walk dimension on connected self-similar sets
Dynamical Systems
2016-09-15 v1
Abstract
Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is an invariant under Lipschitz transforms. As an application, we show some generalized Sierpi\'nski gaskets are not Lipschitz equivalent.
Keywords
Cite
@article{arxiv.1609.04296,
title = {Lipschitz invariance of walk dimension on connected self-similar sets},
author = {Hui Rao and Qingsong Gu},
journal= {arXiv preprint arXiv:1609.04296},
year = {2016}
}
Comments
8 pages, 8 figures