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Expansion properties for finite subdivision rules II


Authors: William Floyd, Walter Parry and Kevin M. Pilgrim
Journal: Conform. Geom. Dyn. 24 (2020), 29-50
MSC (2010): Primary 37F10, 52C20; Secondary 57M12
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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Additional Information

William Floyd
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Email: floyd@math.vt.edu

Walter Parry
Affiliation: Department of Mathematics and Statistics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email: walter.parry@emich.edu

Kevin M. Pilgrim
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: pilgrim@indiana.edu

DOI: https://doi.org/10.1090/ecgd/347
Keywords: Finite subdivision rule, expanding map, postcritically finite, Thurston map
Received by editor(s): August 20, 2019
Received by editor(s) in revised form: November 19, 2019
Published electronically: January 14, 2020
Additional Notes: The third author was supported by Simons grant #245269.
Article copyright: © Copyright 2020 American Mathematical Society