Rational maps whose Julia sets are Cantor circles

被引：13
|
作者：
Qiu, Weiyuan [1 ]
Yang, Fei [2 ]
Yin, Yongcheng [3 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
[3] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2015年 / 35卷
基金：
中国国家自然科学基金;
关键词：
D O I：
10.1017/etds.2013.53
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their corresponding Julia sets. In particular, we give the specific expressions of some rational maps whose Julia sets are Cantor circles, but they are not topologically conjugate to any McMullen maps on their Julia sets. Moreover, some non-hyperbolic rational maps whose Julia sets are Cantor circles are also constructed.
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页码：499 / 529
页数：31
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