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arXiv · 1908.07571

Expansion properties for finite subdivision rules II

William Floyd·Walter Parry·Kevin M. Pilgrim
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Abstract

We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivision map of a finite subdivision rule. We determine which Thurston maps doubly covered by a torus endomorphism have iterates that are isotopic to subdivision maps of finite subdivision rules. We give conditions under which no iterate of a given Thurston map is isotopic to the subdivision map of a finite subdivision rule.

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William Floyd, Walter Parry, Kevin M. Pilgrim. 2019-08-20. Expansion properties for finite subdivision rules II. https://arxiv.org/abs/1908.07571

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