Singular Perturbations with Multiple Poles of the Simple Polynomials
Singular Perturbations with Multiple Poles of the Simple Polynomials
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DOI：
10.1007/s12346-016-0205-0
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发表时间：
2016-06
影响因子：
1.4
通讯作者：
Yingqing Xiao;Fei Yang
中科院分区：
文献类型：
--
作者：
Yingqing Xiao;Fei Yang
在本文中，我们研究以下具有一个参数的有理映射族的动力学：$$\begin{aligned} f_\lambda (z)= z^n+\frac{\lambda ^2}{z^n-\lambda }, \end{aligned}$$其中。这组有理图可以被视为简单多项式的奇异扰动。我们根据自由临界点轨道的动力学行为，描述了该族Julia集的拓扑性质。
In this article, we study the dynamics of the following family of rational maps with one parameter: $$\begin{aligned} f_\lambda (z)= z^n+\frac{\lambda ^2}{z^n-\lambda }, \end{aligned}$$whereand. This family of rational maps can be viewed as a singular perturbations of the simple polynomial. We give a characterization of the topological properties of the Julia sets of the familyaccording to the dynamical behaviors of the orbits of the free critical points.