Nearly Euclidean Thurston maps

We take an in-depth look at Thurston's combinatorial characterization of rational functions for a particular class of maps we call nearly Euclidean Thurston maps. These are orientation-preserving branched maps f\colon S^2\to S^2 and which have exactly four postcritical points. These maps are si...

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Bibliographic Details
Published in:Conformal geometry and dynamics 2012-08, Vol.16 (12), p.209-255
Main Authors: Cannon, J., Floyd, W., Parry, W., Pilgrim, K.
Format: Article
Language:English
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Summary:We take an in-depth look at Thurston's combinatorial characterization of rational functions for a particular class of maps we call nearly Euclidean Thurston maps. These are orientation-preserving branched maps f\colon S^2\to S^2 and which have exactly four postcritical points. These maps are simple enough to be tractable, but are complicated enough to have interesting dynamics.
ISSN:1088-4173
1088-4173
DOI:10.1090/S1088-4173-2012-00248-2