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Rational maps whose Julia sets are Cantor circles

Published online by Cambridge University Press:  19 August 2013

WEIYUAN QIU ,
FEI YANG  and
YONGCHENG YIN
WEIYUAN QIU
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China email wyqiu@fudan.edu.cn
FEI YANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China email yangfei_math@163.com
YONGCHENG YIN
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, PR China email yin@zju.edu.cn
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 2 , April 2015 , pp. 499 - 529
Copyright
© Cambridge University Press, 2013 

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