Teichmüller spaces and holomorphic dynamics

Xavier Buff (1) , Guizhen Cui (2) , Lei Tan (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Institute of Mathematics
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characterization of postcritically finite rational maps. Its proof is a beautiful application of Teichmüller theory. In this chapter we provide a self-contained proof of a slightly generalized version of Thurston's theorem (the marked Thurston's theorem). We also mention some applications and related results, as well as the notion of deformation spaces of rational maps introduced by A. Epstein.

Mots clés: Thurston's theorem; Teichmüller spaces; postcritically finite rational maps; Thurston's theorem.

Domaines: Systèmes dynamiques [math.DS]

Xavier Buff, Guizhen Cui, Lei Tan. Teichmüller spaces and holomorphic dynamics. 2011. ⟨hal-00610715⟩