Lipschitz equivalence of self-similar sets and hyperbolic boundaries

By Jun Jason Luo, Ka-Sing Lau. 2012

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Abstract Kaimanovich (2003)  [9] introduced the concept of augmented tree on the symbolic space of a self-similar 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/137e67fae0d5a98518c4f87a0fbf779e17da84ef