Lipschitz invariance of walk dimension on connected self-similar sets

Hui Rao; Qingsong Gu

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arXiv · 1609.04296

Lipschitz invariance of walk dimension on connected self-similar sets

Hui Rao·Qingsong Gu

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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.

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Hui Rao, Qingsong Gu. 2016-09-14. Lipschitz invariance of walk dimension on connected self-similar sets. https://arxiv.org/abs/1609.04296

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