A Characterization of Hyperbolic Affine Iterated Function Systems
Geometric Topology
2009-08-12 v1
Abstract
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-similar set, does there exist an associated system of contraction mappings? Our theorems imply an affirmative answer to Kameyama's question for self-similar sets derived from affine transformations on Rm.
Cite
@article{arxiv.0908.1416,
title = {A Characterization of Hyperbolic Affine Iterated Function Systems},
author = {Ross Atkins and Michael F. Barnsley and Andrew Vince and David C. Wilson},
journal= {arXiv preprint arXiv:0908.1416},
year = {2009}
}