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Twisted matings and equipotential gluings

Xavier BuffAdam L. EpsteinSarah Koch — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

One crucial tool for studying postcritically finite rational maps is Thurston’s topological characterization of rational maps. This theorem is proved by iterating a holomorphic endomorphism on a certain Teichmüller space. The graph of this endomorphism covers a correspondence on the level of moduli space. In favorable cases, this correspondence is the graph of a map, which can be used to study matings. We illustrate this by way of example: we study the mating of the basilica with itself.

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