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Title:
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On a family of rational perturbations of the doubling map
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Author:
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Canela Sánchez, Jordi; Fagella Rabionet, Núria; Garijo Real, Antonio
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Other authors:
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Universitat de Barcelona |
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Abstract:
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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. |
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Subject(s):
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-Sistemes dinàmics diferenciables
-Funcions de variables complexes
-Dinàmica topològica
-Fractals
-Differentiable dynamical systems
-Functions of complex variables
-Topological dynamics
-Fractals |
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Rights:
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(c) Taylor and Francis, 2015
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Document type:
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Article
Article - Accepted version |
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Published by:
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Taylor and Francis
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