A Characterization of Hyperbolic Affine Iterated Function Systems

Ross Atkins; Michael F. Barnsley; Andrew Vince; David C. Wilson

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arXiv · 0908.1416

A Characterization of Hyperbolic Affine Iterated Function Systems

Ross Atkins·Michael F. Barnsley·Andrew Vince·David C. Wilson

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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.

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Ross Atkins, Michael F. Barnsley, Andrew Vince, David C. Wilson. 2009-08-10. A Characterization of Hyperbolic Affine Iterated Function Systems. https://arxiv.org/abs/0908.1416

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