Nearly Euclidean Thurston maps

J. W. Cannon, W. J. Floyd, W. R. Parry and K. M. Pilgrim
April 16, 2012


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 from the 2-sphere into itself 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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