Displaying similar documents to “Matings and the other side of the dictionary”

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.

Introduction

Pascale Roesch (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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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.

Tan Lei and Shishikura’s example of non-mateable degree 3 polynomials without a Levy cycle

Arnaud Chéritat (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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After giving an introduction to the procedure dubbed and quickly recalling known results about more classical notions of polynomial mating, we show conformally correct pictures of the slow mating of two degree 3 post critically finite polynomials introduced by Shishikura and Tan Lei as an example of a non matable pair of polynomials without a Levy cycle. The pictures show a limit for the Julia sets, which seems to be related to the Julia set of a degree 6 rational map. We give a conjectural...

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.