Expansion properties for finite subdivision rules II
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- by William Floyd, Walter Parry and Kevin M. Pilgrim PDF
- Conform. Geom. Dyn. 24 (2020), 29-50 Request permission
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.References
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Additional Information
- William Floyd
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 67750
- Email: floyd@math.vt.edu
- Walter Parry
- Affiliation: Department of Mathematics and Statistics, Eastern Michigan University, Ypsilanti, Michigan 48197
- MR Author ID: 136390
- Email: walter.parry@emich.edu
- Kevin M. Pilgrim
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 614176
- Email: pilgrim@indiana.edu
- 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.
- © Copyright 2020 American Mathematical Society
- Journal: Conform. Geom. Dyn. 24 (2020), 29-50
- MSC (2010): Primary 37F10, 52C20; Secondary 57M12
- DOI: https://doi.org/10.1090/ecgd/347
- MathSciNet review: 4051834