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arXiv · 1206.6171

Graphs induced by iterated function systems

Xiang-Yang Wang
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Abstract

For an iterated function system (IFS) of simillitidues, we define two graphs on the representing symbolic space. We show that if the self-similar set $K$ has positive Lebesgue measure or the IFS satisfies the weak separation condition, then the graphs are hyperbolic, moreover the hyperbolic boundaries are homeomorphic to the self-similar sets.

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Xiang-Yang Wang. 2012-06-27. Graphs induced by iterated function systems. https://arxiv.org/abs/1206.6171

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