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http://hdl.handle.net/2445/67324
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 Fractals Differentiable dynamical systems Functions of complex variables Topological dynamics Fractals |
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 |
URI: | http://hdl.handle.net/2445/67324 |
Related resource: | http://dx.doi.org/10.1080/10236198.2015.1050387 |
ISSN: | 1023-6198 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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654852.pdf | 1.63 MB | Adobe PDF | View/Open |
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