Convergence of pinching deformations and matings of geometrically finite polynomials

• Autorzy: Peter Haïssinsky , Lei Tan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F10: Polynomials; rational maps; entire and meromorphic functions
• 37F30: Quasiconformal methods and Teichm\"uller theory; Fuchsian and Kleinian groups as dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 2
• Strony: 143-188

Daty

wydano

2004

Twórcy

autor

Peter Haïssinsky

• LATP/CMI, Université de Provence, 39, rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13, France

autor

Lei Tan

• Unité CNRS-UMR 8088, Département de Mathématiques, Université de Cergy-Pontoise, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

Identyfikatory

DOI

10.4064/fm181-2-4