Characterizations of contracting Hurwitz bisets
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 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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