10 citations · 29 across the 12 of their papers we have counts for
18 papers
Characterizations of contracting Hurwitz bisets
Walter Parry, Kevin M. Pilgrim
A critically finite branched self-cover determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at…
Realizing polynomial portraits
William Floyd, Daniel Kim, Sarah Koch +2
It is well known that the dynamical behavior of a rational map is governed by the forward orbits of the critical points of . The m…
Expansion properties for finite subdivision rules II
William Floyd, Walter Parry, Kevin M. Pilgrim
We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivi…
Rationality is decidable for nearly Euclidean Thurston maps
William Floyd, Walter Parry, Kevin M. Pilgrim
Nearly Euclidean Thurston (NET) maps are described by simple diagrams which admit a natural notion of size. Given a size bound , there are finitely many diagrams of size at most…
NET map slope functions
Walter Parry
This paper studies NET map slope functions. It establishes Lipschitz-type conditions for them. It relates Lipschitz-type conditions to the half-space theorem. It gives bounds on th…
Modular groups, Hurwitz classes and dynamic portraits of NET maps
William Floyd, Walter Parry, Kevin M. Pilgrim
An orientation-preserving branched covering is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four poi…