Branched coverings and cubic Newton maps

Lei Tan

Displaying similar documents to “Branched coverings and cubic Newton maps”

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...

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

Petracovici, Lia (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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Remarks on the simple connectedness of basins of sinks for iterations of rational maps

Feliks Przytycki (1989)

Banach Center Publications

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Fractal Newton basins.

Sahari, M.L., Djellit, I. (2006)

Discrete Dynamics in Nature and Society

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

Milnor, John (2004)

Experimental Mathematics

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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 pinching deformations of rational maps

Lei Tan (2002)

Annales scientifiques de l'École Normale Supérieure

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