Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/67324
 Title: On a family of rational perturbations of the doubling map Author: Canela Sánchez, JordiFagella Rabionet, NúriaGarijo Real, Antonio Keywords: Sistemes dinàmics diferenciablesFuncions de variables complexesDinàmica topològicaFractalsDifferentiable dynamical systemsFunctions of complex variablesTopological dynamicsFractals 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: http://dx.doi.org/10.1080/10236198.2015.1050387 It is part of: Journal of Difference Equations and Applications, 2015, vol. 21, num. 8, p. 715-741 Related resource: http://dx.doi.org/10.1080/10236198.2015.1050387 URI: http://hdl.handle.net/2445/67324 ISSN: 1023-6198 Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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