Algorithmic construction of Hurwitz maps

TL;DR

This paper presents an algorithm that constructs precise complex approximations of rational maps from permutation data, enabling new computational approaches in dynamical systems research.

Contribution

It introduces a novel algorithm for constructing rational maps from permutation monodromy data, advancing computational methods in complex dynamics.

Findings

Successfully constructs accurate rational map approximations from permutation data

Enables computational exploration of dynamical systems problems

Applied to study a problem raised by Cui

Abstract

We describe an algorithm that, given a k-tuple of permutations representing the monodromy of a rational map, constructs an arbitrarily precise floating-point complex approximation of that map. We then explain how it has been used to study a problem in dynamical systems raised by Cui.