Thurston equivalence to a rational map is decidable

TL;DR

This paper proves that it is possible to algorithmically determine whether a given postcritically finite topological map on the sphere is equivalent to a rational map, solving a longstanding decision problem in complex dynamics.

Contribution

It establishes the decidability of Thurston equivalence to rational maps for postcritically finite topological maps, a major theoretical advancement.

Findings

Decidability of Thurston equivalence proven

Algorithm exists to determine rational map equivalence

Advances understanding of complex dynamics and topological classification

Abstract

We demonstrate that the question whether or not a given postcritically finite topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.