Latt\`es maps and combinatorial expansion

TL;DR

This paper characterizes Lattès maps, which are rational maps derived from torus endomorphisms, by analyzing their combinatorial expansion properties, providing a new perspective on their dynamical behavior.

Contribution

It introduces a novel characterization of Lattès maps based on their combinatorial expansion, linking geometric structure with dynamical properties.

Findings

Lattès maps can be distinguished by their unique combinatorial expansion behavior.

The paper establishes criteria connecting conformal torus endomorphisms to rational maps.

New insights into the dynamics of Lattès maps are provided through combinatorial analysis.

Abstract

A Latt\`es map $f\colon \hat{\mathbb{C}}\rightarrow \hat{\mathbb{C}}$ is a rational map that is obtained from a finite quotient of a conformal torus endomorphism. We characterize Latt\`es maps by their combinatorial expansion behavior.