Lipschitz equivalence of self-similar sets and hyperbolic boundaries

Jun Luo Shantou University Ka-Sing Lau The Chinese University of Hong Kong

Geometric Analysis and Geometric Topology mathscidoc:1702.15001

Advances in Mathematics, 235, 2013
Kaimanovich (2003) [9] introduced the concept of augmented tree on the symbolic space of a selfsimilar set. It is hyperbolic in the sense of Gromov, and it was shown by Lau and Wang (2009) [12] that under the open set condition, a self-similar set can be identified with the hyperbolic boundary of the tree. In the paper, we investigate in detail a class of simple augmented trees and the Lipschitz equivalence of such trees. The main purpose is to use this to study the Lipschitz equivalence problem of the totally disconnected self-similar sets which has been undergoing some extensive development recently.
Augmented tree; Hyperbolic boundary; Incidence matrix; Lipschitz equivalence; OSC; Primitive; Rearrangeable; Self-similar set; Self-affine set
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  title={Lipschitz equivalence of self-similar sets and hyperbolic boundaries},
  author={Jun Luo, and Ka-Sing Lau},
  booktitle={Advances in Mathematics},
Jun Luo, and Ka-Sing Lau. Lipschitz equivalence of self-similar sets and hyperbolic boundaries. 2013. Vol. 235. In Advances in Mathematics.
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