On McMullen-like mappings
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Godillon, Sebastién (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)

Date:	2015
Abstract:	We introduce a generalization of the McMullen family f_(z) = z^n /zd^. In 1988 C. McMullen showed that the Julia set of f_ is a Cantor set of circles if and only if 1/n 1/d < 1 and the simple critical values of f_ belong to the trap door. We generalize this behavior and we define a McMullen-like mapping as a rational map f associated to a hyperbolic postcritically finite polynomial P and a pole data D where we encode, basically, the location of every pole of f and the local degree at each pole. In the McMullen family the polynomial P is z z^n and the pole data D is the pole located at the origin that maps to infinity with local degree d. As in the McMullen family f_ we can characterize a McMullen-like mapping using an arithmetic condition depending only on the polynomial P and the pole data D. We prove that the arithmetic condition is necessary using the theory of Thurston's obstructions, and sufficient by quasiconformal surgery.
Grants:	Ministerio de Economía y Competitividad MTM2008-01486 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Complex dynamics ; Julia sets ; McMullen family ; Rational maps
Published in:	Journal of Fractal Geometry, Vol. 2 (2015) , p. 249-279, ISSN 2308-1317

Postprint 21 p, 1.2 MB

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