Blaschke积的奇异扰动与Fatou分支的连通性
Singular perturbations of Blaschke Products and connectivity of Fatou components
摘要：
本文的目的是研究由$B_{a,λ}(z)=z^3\frac{z-a}{1-\overline{a}z}+\fracλ{z^2}$给出的Blaschke积的奇异扰动族。我们专注于研究这些合理的映射参数$a$在穿孔磁盘$\mathbb{D}^*$和$|λ|$小。证明了在一定条件下，奇摄动Blaschke积$B_{a,λ}$的所有Fatou分量都具有有限连通性，但在其动力平面内存在任意大连通性的分量.在同样的条件下，我们证明了朱利亚集是可数多个拟圆的Cantor集与不可数多个点连通集的并.
英文摘要：
The goal of this paper is to study the family of singular perturbations of Blaschke products given by $B_{a,λ}(z)=z^3\frac{z-a}{1-\overline{a}z}+\fracλ{z^2}$. We focus on the study of these rational maps for parameters $a$ in the punctured disk $\mathbb{D}^*$ and $|λ|$ small. We prove that, under certain conditions, all Fatou components of a singularly perturbed Blaschke product $B_{a,λ}$ have finite connectivity but there are components of arbitrarily large connectivity within its dynamical plane. Under the same conditions we prove that the Julia set is the union of countably many Cantor sets of quasicircles and uncountably many point components.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
