Teichmüller spaces and holomorphic dynamics

  • Xavier Buff

    Université Paul Sabatier, Toulouse, France
  • Guizhen Cui

    Chinese Academy of Sciences, Beijing, China
  • Lei Tan

    Université d'Angers, France
Teichmüller spaces and holomorphic dynamics cover

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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.