English

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 KK 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.

Keywords

Cite

@article{arxiv.1206.6171,
  title  = {Graphs induced by iterated function systems},
  author = {Xiang-Yang Wang},
  journal= {arXiv preprint arXiv:1206.6171},
  year   = {2012}
}
R2 v1 2026-06-21T21:26:09.886Z