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Thurston equivalence for rational maps with clusters
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Sharland, Thomas Joseph (2013) Thurston equivalence for rational maps with clusters. Ergodic Theory and Dynamical Systems, Volume 33 (Number 04). pp. 1178-1198. doi:10.1017/S0143385712000181 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385712000181
Abstract
We investigate rational maps with period-one and period-two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is d and the cluster is fixed, the Thurston class of a rational map is fixed by the combinatorial rotation number ρ and the critical displacement δof the cluster cycle. The same result will also be proved in the case where the rational map is quadratic and has a period-two cluster cycle, and we will also show that the statement is no longer true in the higher-degree case.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Dynamics, Mathematics | ||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0143-3857 | ||||
Official Date: | August 2013 | ||||
Dates: |
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Volume: | Volume 33 | ||||
Number: | Number 04 | ||||
Page Range: | pp. 1178-1198 | ||||
DOI: | 10.1017/S0143385712000181 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 25 December 2015 | ||||
Date of first compliant Open Access: | 25 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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