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arXiv · 1403.3489

Lipschitz equivalence of self-similar sets and hyperbolic boundaries II

Guo-Tai Deng·Ka-Sing Lau·Jun Jason Luo
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Abstract

In \cite{LuLa13}, two of the authors initiated a study of Lipschitz equivalence of self-similar sets through the augmented trees, a class of hyperbolic graphs introduced by Kaimanovich \cite{Ka03} and developed by Lau and Wang \cite{LaWa09}. In this paper, we continue such investigation. We remove a major assumption in the main theorem in \cite{LuLa13} by using a new notion of quasi-rearrangeable matrix, and show that the hyperbolic boundary of any simple augmented tree is Lipschitz equivalent to a Cantor-type set. We then apply this result to consider the Lipschitz equivalence of certain totally disconnected self-similar sets as well as their unions.

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Guo-Tai Deng, Ka-Sing Lau, Jun Jason Luo. 2014-08-17. Lipschitz equivalence of self-similar sets and hyperbolic boundaries II. https://arxiv.org/abs/1403.3489

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