Non-accessible critical points of certain rational functions with Cremer points.

Petracovici, Lia

Displaying similar documents to “Non-accessible critical points of certain rational functions with Cremer points.”

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.

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...

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.

On a theorem of Rees-Shishikura

Guizhen Cui, Wenjuan Peng, Lei Tan (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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Rees-Shishikura’s theorem plays an important role in the study of matings of polynomials. It promotes Thurston’s combinatorial equivalence into a semi-conjugacy. In this work we restate and reprove Rees-Shishikura’s theorem in a more general form, which can then be applied to a wider class of postcritically finite branched coverings. We provide an application of the restated theorem.

Hyperbolic components of polynomials with a fixed critical point of maximal order

Pascale Roesch (2007)

Annales scientifiques de l'École Normale Supérieure

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Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric.

Zoltán M. Balogh, Matthieu Rickly, Francesco Serra Cassano (2003)

Publicacions Matemàtiques

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We compare the Hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The sharpness of our estimates is shown by examples. Moreover a comparison between Euclidean and H-rectifiability is given.