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On the dynamics of generalized McMullen maps

Published online by Cambridge University Press:  05 June 2013

YINGQING XIAO ,
WEIYUAN QIU  and
YONGCHENG YIN
YINGQING XIAO
Affiliation:
College of Mathematics and Economics, Hunan University, Changsha, 410082, China email [email protected]
WEIYUAN QIU
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China email [email protected]
YONGCHENG YIN
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, China email [email protected]
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Abstract

In this paper, we study the dynamics of the two-parameter family of rational maps

$$\begin{eqnarray*}{F}_{a, b} (z)= {z}^{n} + \frac{a}{{z}^{n} } + b.\end{eqnarray*}$$
We give the topological description of Julia sets and Fatou components of ${F}_{a, b} $ according to the dynamical behavior of the orbits of its free critical points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 6 , December 2014 , pp. 2093 - 2112
Copyright
© Cambridge University Press, 2013 

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