Expansion properties for finite subdivision rules II

Floyd, William; Parry, Walter; Pilgrim, Kevin

doi:10.1090/ecgd/347

Expansion properties for finite subdivision rules II
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by William Floyd, Walter Parry and Kevin M. Pilgrim

Conform. Geom. Dyn. 24 (2020), 29-50

DOI: https://doi.org/10.1090/ecgd/347

Published electronically: January 14, 2020

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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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