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Branched coverings and cubic Newton maps

100%

Tan L.

Fundamenta Mathematicae

1997

tom 154

nr 3

207-260

We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).

Convergence of pinching deformations and matings of geometrically finite polynomials

63%

Haïssinsky P., Tan L.

Fundamenta Mathematicae

2004

tom 181

nr 2

143-188

We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials radially, and do not belong to conjugate limbs of the Mandelbrot set, then their mating exists and deforms continuously to the mating of the two root polynomials.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Tan L.

1 Haïssinsky P.

1 2004

1 1997

Wyniki wyszukiwania

Branched coverings and cubic Newton maps

Convergence of pinching deformations and matings of geometrically finite polynomials