Lipschitz invariance of walk dimension on connected self-similar sets

2016/09/14 by Hui Rao, Rao, Hui, Qingsong Gu +1 · 2 citations
Computer Science · Mathematics · #35J08 #46E35 #47D07 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 35K08 Secondary: 28A80 #Topological and Geometric Data Analysis #math.DS #msc:28A80 #msc:35J08 #msc:35K08 #msc:46E35 #msc:47D07

paper · pdf · doi:10.48550/arxiv.1609.04296

8 pages, 8 figures

arxiv created 2016/09/14 · openalex publication_date 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Sierpiński gaskets are not Lipschitz equivalent.

Cited by

• Lipschitz equivalence of fractals and finite state automaton
• A Localized Diffusive Time Exponent for Compact Metric Spaces

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