Teichmüller spaces and holomorphic dynamics
Xavier BuffUniversité Paul Sabatier, Toulouse, France
Guizhen CuiChinese Academy of Sciences, Beijing, China
Lei TanUniversité d'Angers, France
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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.