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Title: On a family of rational perturbations of the doubling map
Author: Canela Sánchez, Jordi
Fagella Rabionet, Núria
Garijo Real, Antonio
Keywords: Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
Issue Date: 17-Jun-2015
Publisher: Taylor and Francis
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 $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. 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 $\left(\overline{\overline{z}^2+c}\right)^2+c$. In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type.
Note: Versió postprint del document publicat a:
It is part of: Journal of Difference Equations and Applications, 2015, vol. 21, num. 8, p. 715-741
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ISSN: 1023-6198
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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