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Déformation J-équivalente de polynômes géometriquement finis

100%

Haïssinsky P.

Fundamenta Mathematicae

2000

tom 163

nr 2

131-141

Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.

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 Haïssinsky P.

1 Tan L.

1 2004

1 2000

Wyniki wyszukiwania

Déformation J-équivalente de polynômes géometriquement finis

Convergence of pinching deformations and matings of geometrically finite polynomials