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arXiv · 1501.03647

On a Family of Rational Perturbations of the Doubling Map

Jordi Canela·Núria Fagella·Antonio Garijo
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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.

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Jordi Canela, Núria Fagella, Antonio Garijo. 2015-01-15. On a Family of Rational Perturbations of the Doubling Map. https://doi.org/10.1080/10236198.2015.1050387

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