Characterizations of contracting Hurwitz bisets

Walter Parry; Kevin M. Pilgrim

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arXiv · 2506.23222

Characterizations of contracting Hurwitz bisets

Walter Parry·Kevin M. Pilgrim

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Abstract

A critically finite branched self-cover $f: (S^2, P) \to (S^2, P)$ determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at $P$, one on the Teichm\"uller 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.

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Walter Parry, Kevin M. Pilgrim. 2025-06-29. Characterizations of contracting Hurwitz bisets. https://arxiv.org/abs/2506.23222

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