Lipschitz equivalence of self-similar sets with touching structures

Huo-Jun Ruan; Yang Wang; Li-Feng Xi

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arXiv · 1207.6674

Lipschitz equivalence of self-similar sets with touching structures

Huo-Jun Ruan·Yang Wang·Li-Feng Xi

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Abstract

Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much more challenging and intriguing at the same time. So far the only known results only cover self-similar sets in $\bR$ with no more than 3 branches. In this study we establish results for the Lipschitz equivalence of self-similar sets with touching structures in $\bR$ with arbitrarily many branches. Key to our study is the introduction of a geometric condition for self-similar sets called {\em substitutable}.

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BibTeX RIS

Huo-Jun Ruan, Yang Wang, Li-Feng Xi. 2012-07-28. Lipschitz equivalence of self-similar sets with touching structures. https://arxiv.org/abs/1207.6674

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