Presentations of NET maps

2017/01/02 by Floyd, William, Parry, Walter, Pilgrim, Kevin M. · 1 citation
#36F10 #57M12 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.00443

Abstract

A branched covering f: S² → S² is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four points. We show that up to equivalence, each NET map admits a normal form in terms of simple affine data. This data can then be used as input for algorithms developed for the computation of fundamental invariants, now systematically tabulated in a large census.

Cited by

• Characterizations of contracting Hurwitz bisets

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• Modular groups, Hurwitz classes and dynamic portraits of NET maps
• On Net Maps: Examples and Nonexistence Results
• Nearly Euclidean Thurston maps
• Rationality is decidable for nearly Euclidean Thurston maps
• Algorithmic aspects of branched coverings