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Singular perturbations of the unicritical polynomials with two parameters

Published online by Cambridge University Press:  12 January 2016

YINGQING XIAO  and
FEI YANG
YINGQING XIAO
Affiliation:
College of Mathematics and Economics, Hunan University, Changsha 410082, PR China email [email protected]
FEI YANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China email [email protected]
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Abstract

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In this paper, we study the dynamics of the family of rational maps with two parameters

$$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$
where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 6 , September 2017 , pp. 1997 - 2016
Copyright
© Cambridge University Press, 2016 

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