On a Family of Rational Perturbations of the Doubling Map

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Title:	On a Family of Rational Perturbations of the Doubling Map
Author:	Canela Sánchez, Jordi; Fagella Rabionet, Núria; Garijo, Antoni
Abstract:	Agraïments: The three actors were supported by MTM2011-26995-C02-02 and EU Project MRTN-CT-2006-035651 and FPU AP-2009-4564
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.
Subject(s):	-Blaschke products -Circle maps -Holomorphic dynamics -Polynomial-like mappings
Rights:	open access Tots els drets reservats. https://rightsstatements.org/vocab/InC/1.0/
Document type:	Article
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Uri:	https://ddd.uab.cat/record/145290