Pasting together Julia sets: a worked out example of mating.

Milnor, John

Displaying similar documents to “Pasting together Julia sets: a worked out example of mating.”

A classification of bicritical rational maps with a pair of period two superattracting cycles

Adam Epstein, Thomas Sharland (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree $d$ polynomials.

Hyperbolicity of renormalization of critical circle maps

Michael Yampolsky (2003)

Publications Mathématiques de l'IHÉS

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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...

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

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Let $H^{d}$ be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if $f \in H^{d}$ and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of $H^{d}$ containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate...

Fixed points of polynomial maps. Part II. Fixed point portraits

Lisa R. Goldberg, John Milnor (1993)

Annales scientifiques de l'École Normale Supérieure

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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.