Affiliation:
1. School of Science, China University of Mining and Technology, Beijing 100083, China
2. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang 421002, China
Abstract
I. N. Baker established the existence of Fatou component with any given finite connectivity by the method of quasi-conformal surgery. M. Shishikura suggested giving an explicit rational map which has a Fatou component with finite connectivity greater than 2. In this paper, considering a family of rational mapsRz,tthat A. F. Beardon proposed, we prove thatRz,thas Fatou components with connectivities 3 and 5 for anyt∈0,1/12. Furthermore, there existst∈0,1/12such thatRz,thas Fatou components with connectivity nine.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献