Displaying similar documents to “An algebraic formulation of Thurston’s characterization of rational functions”

Twisted matings and equipotential gluings

Xavier Buff, Adam L. Epstein, Sarah Koch (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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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. ...

A lantern lemma.

Margalit, Dan (2002)

Algebraic & Geometric Topology

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Questions about Polynomial Matings

Xavier Buff, Adam L. Epstein, Sarah Koch, Daniel Meyer, Kevin Pilgrim, Mary Rees, Tan Lei (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We survey known results about polynomial mating, and pose some open problems.

Captures, matings and regluings

Inna Mashanova, Vladlen Timorin (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.

On The Notions of Mating

Carsten Lunde Petersen, Daniel Meyer (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.