On thurston's core entropy algorithm dedicated to the memory of tan lei

TL;DR

This paper describes and proves the validity of Thurston's combinatorial algorithm for computing the core entropy of complex polynomials, a key dynamical invariant extending topological entropy.

Contribution

It provides a rigorous proof of Thurston's core entropy algorithm, establishing its correctness for studying polynomial parameter spaces.

Findings

Proof of the validity of Thurston's core entropy algorithm

Clarification of the algorithm's steps and mathematical foundation

Enhancement of tools for analyzing polynomial dynamics

Abstract

The core entropy of polynomials, recently introduced by W. Thurston, is a dy-namical invariant extending topological entropy for real maps to complex polynomials, whence providing a new tool to study the parameter space of polynomials. The base is a combinatorial algorithm allowing for the computation of the core entropy given by Thurston, but without supplying a proof. In this paper, we will describe his algorithm and prove its validity.