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On a family of rational perturbations of the doubling map
Canela Sánchez, Jordi; Fagella Rabionet, Núria; Garijo Real, Antonio
Universitat de Barcelona
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.
Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Fractals
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
Fractals
(c) Taylor and Francis, 2015
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