Modular groups, Hurwitz classes and dynamic portraits of NET maps
Dynamical Systems
2017-03-14 v1
Abstract
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 points. Inspired by classical, non-dynamical notions such as Hurwitz equivalence of branched covers of surfaces, we develop invariants for such maps. We then apply these notions to the classification and enumeration of NET maps. As an application, we obtain a complete classification of the dynamic critical orbit portraits of NET maps.
Cite
@article{arxiv.1703.03983,
title = {Modular groups, Hurwitz classes and dynamic portraits of NET maps},
author = {William Floyd and Walter Parry and Kevin M. Pilgrim},
journal= {arXiv preprint arXiv:1703.03983},
year = {2017}
}