A Characterization of Hyperbolic Affine Iterated Function Systems

Details A Characterization of Hyperbolic Affine Iterated Function Systems A Characterization of Hyperbolic Affine Iterated Function Systems

2009-08-10

arxiv.org/abs/0908.1416v1

Mathematics

Geometric Topology

Scientific paper

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.

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