Galois conjugates of entropies of real unimodal maps

TL;DR

This paper studies the Galois conjugates of growth rates of superattracting real quadratic polynomials, proving their set is both path-connected and locally connected, revealing topological properties of these algebraic numbers.

Contribution

It establishes the topological structure of the set of Galois conjugates of these growth rates, a novel insight in complex dynamics and number theory.

Findings

The closure of the set of Galois conjugates is path-connected.

The set of Galois conjugates is locally connected.

The work extends understanding of algebraic properties of dynamical systems.

Abstract

We investigate the set of Galois conjugates of growth rates of superattracting real quadratic polynomials, following W. Thurston. In particular, we prove that the closure of this set is path-connected and locally connected.