IUMJ

Title: Self-similar sets as hyperbolic boundaries

Authors: Ka-Sing Lau and Xiang-Yang Wang

Issue: Volume 58 (2009), Issue 4, 1777-1796

Abstract:

We show that, for an iterated function system $\{S_j\}_{j=1}^N$ of similitudes that satisfies the open set condition, there is a natural graph structure in the representing symbolic space to make it a hyperbolic graph, and the hyperbolic boundary is homeomorphic to the self-similar set generated by $\{S_j\}_{j=1}^N$.