Nearly Euclidean Thurston maps

Cannon, J.; Floyd, W.; Parry, W.; Pilgrim, K.

doi:10.1090/S1088-4173-2012-00248-2

Nearly Euclidean Thurston maps
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by J. W. Cannon, W. J. Floyd, W. R. Parry and K. M. Pilgrim

Conform. Geom. Dyn. 16 (2012), 209-255

DOI: https://doi.org/10.1090/S1088-4173-2012-00248-2

Published electronically: August 15, 2012

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Abstract:

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 $f\colon S^2\to S^2$ whose local degree at every critical point is $2$ and which have exactly four postcritical points. These maps are simple enough to be tractable, but are complicated enough to have interesting dynamics.

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