Self-similar sets as hyperbolic boundaries
Ka-Sing LauXiang-Yang Wang
28A7828A80boundarygeodesic rayhyperbolic graphiterated function systemself-similar setsopen set condition
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 $\{S_j\}_{j=1}^N$.
Indiana University Mathematics Journal
2009
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10.1512/iumj.2009.58.3639
10.1512/iumj.2009.58.3639
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Indiana Univ. Math. J. 58 (2009) 1777 - 1796
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