Hyperbolicity of renormalization of critical circle maps

Michael Yampolsky

Displaying similar documents to “Hyperbolicity of renormalization of critical circle maps”

Structurally stable perturbations of polynomials in the Riemann sphere

J. Iglesias, A. Portela, A. Rovella (2008)

Annales de l'I.H.P. Analyse non linéaire

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

Milnor, John (2004)

Experimental Mathematics

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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.

Rigidity and renormalization in one dimensional dynamical systems.

de Melo, W. (1998)

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On unimodal maps with critical order 2 + ε

Simin Li, Weixiao Shen (2006)

Fundamenta Mathematicae

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It is proved that a smooth unimodal interval map with critical order 2 + ε has no wild attractor if ε >0 is small.

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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On pinching deformations of rational maps

Lei Tan (2002)

Annales scientifiques de l'École Normale Supérieure

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