A characterization of Sierpinski carpet Rational maps

TL;DR

This paper characterizes when postcritically finite rational maps with non-empty Fatou sets are Thurston equivalent to expanding Thurston maps, based on the topological structure of their Julia sets being homeomorphic to the Sierpinski carpet.

Contribution

It establishes a precise topological criterion linking Julia set homeomorphism to the Thurston equivalence class of rational maps.

Findings

Julia set homeomorphic to Sierpinski carpet iff Thurston equivalent to an expanding Thurston map

Provides a topological characterization of certain rational maps

Connects Julia set topology with dynamical equivalence classes

Abstract

In this paper, we prove that a postcritically finite rational map with non-empty Fatou set is Thurstion equivalent to an expanding Thurston map if and only if its Julia set is homeomorphic to the standard Sierpinski carpet