Dessins d'enfants and Hubbard trees

Abstract

We show that the absolute Galois group acts faithfully on the set of Hubbard trees. Hubbard trees are finite planar trees, equipped with self-maps, which classify postcritically finite polynomials as holomorphic dynamical systems on the complex plane. We establish an explicit relationship between certain Hubbard trees and the trees known as "dessins d'enfants" introduced by Grothendieck. © 2000 Éditions scientifiques et médicales Elsevier SAS.