On a family of rational perturbations of the doubling map
On a family of rational perturbations of the doubling map
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DOI：
10.1080/10236198.2015.1050387
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发表时间：
2015-01
影响因子：
1.1
通讯作者：
Jordi Canela;N. Fagella;A. Garijo
中科院分区：
文献类型：
--
作者：
Jordi Canela;N. Fagella;A. Garijo
本文的目的是研究由Blaschke乘积给出的加倍映射的有理扰动族的参数平面。首先，我们研究了这些映射的基本性质，如Julia集作为参数a的函数的连通性。我们使用拟共形手术的技术，探讨某些家庭成员和4次多项式之间的关系。在参数空间中，我们根据临界轨道对不同的双曲分量进行了分类，并展示了如何对不相交类型的双曲分量进行参数化。
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 . 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 . In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type.