Lipschitz invariance of walk dimension on connected self-similar sets

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...

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Bibliographic Details
Main Authors:	Rao, Hui, Gu, Qingsong
Format:	Journal Article
Language:	English
Published:	14-09-2016
Subjects:	Mathematics - Dynamical Systems
Online Access:	Get full text
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Summary:	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.
DOI:	10.48550/arxiv.1609.04296