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Teichmüller spaces and holomorphic dynamics

Abstract : 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.
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Preprints, Working Papers, ...
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Submitted on : Saturday, July 23, 2011 - 7:16:32 PM
Last modification on : Monday, July 4, 2022 - 10:22:27 AM
Long-term archiving on: : Sunday, December 4, 2016 - 7:09:04 AM


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  • HAL Id : hal-00610715, version 1


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



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