Thurston type Theorem for sub-hyperbolic rational maps

TL;DR

This paper provides a simplified proof of Thurston's theorem extended to sub-hyperbolic rational maps, offering a clearer understanding of their combinatorial characterization.

Contribution

It introduces a new, simpler proof of the Thurston type theorem for sub-hyperbolic rational maps, building on existing extensions.

Findings

Simplified proof of Thurston's theorem for sub-hyperbolic maps

Clarification of combinatorial characterization

Enhanced understanding of rational map dynamics

Abstract

In 1980's, Thurston established a combinatorial characterization for post-critically finite rational maps. This criterion was then extended by Cui, Jiang, and Sullivan to sub-hyperbolic rational maps. The goal of this paper is to present a new but simpler proof of this result by adapting the argument in the proof of Thurston's Theorem.