Graphs induced by iterated function systems
Functional Analysis
2012-06-28 v1
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 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.
Cite
@article{arxiv.1206.6171,
title = {Graphs induced by iterated function systems},
author = {Xiang-Yang Wang},
journal= {arXiv preprint arXiv:1206.6171},
year = {2012}
}