On a Family of Rational Perturbations of the Doubling Map
Canela Sánchez, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2015
Abstract:	The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the parameter a. We use techniques of quasiconformal surgery to explore the relation between certain members of the family and the degree 4 polynomials. In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792
Note:	Agraïments: The three actors were supported by MTM2011-26995-C02-02 and EU Project MRTN-CT-2006-035651 and FPU AP-2009-4564
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Blaschke products ; Circle maps ; Holomorphic dynamics ; Polynomial-like mappings
Published in:	Journal of Difference Equations and Applications, Vol. 21 Núm. 8 (2015) , p. 715-741, ISSN 1563-5120

DOI: 10.1080/10236198.2015.1050387

Postprint 30 p, 1.8 MB

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