Characterizations of contracting Hurwitz bisets

2025/06/29 by Parry, Walter, Pilgrim, Kevin M.
#37F #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.23222

Abstract

A critically finite branched self-cover f: (S², P) → (S², P) determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at P, one on the Teichmüller space of the sphere marked at P, and one on a finite-dimensional real vector space. We show that contraction for any one of these systems implies contraction for the others.

Citations

• Critically fixed Thurston maps: classification, recognition, and twisting
• Rationality is decidable for nearly Euclidean Thurston maps
• Modular groups, Hurwitz classes and dynamic portraits of NET maps
• Presentations of NET maps
• Algorithmic aspects of branched coverings IV/V. Expanding maps
• Algorithmic aspects of branched coverings I. Van Kampen's Theorem for\n bisets
• A note on the Joint Spectral Radius
• On the classification of critically fixed rational maps
• Pullback invariants of Thurston maps
• Boundary Values of the Thurston Pullback Map
• Nearly Euclidean Thurston maps
• Combinatorial models of expanding dynamical systems
• Geometry of the mapping class groups I: Boundary amenability
• Self-similar groups and topological dimension

Related

• Realizations of self branched coverings of the 2-sphere
• Algorithmic aspects of branched coverings II/V. Sphere bisets and their decompositions
• Algorithmic aspects of branched coverings I. Van Kampen's Theorem for\n bisets
• Bijections for simple and double Hurwitz numbers
• Modular groups, Hurwitz classes and dynamic portraits of NET maps