期刊论文

Wang, Youming

英文

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

1078-0947

2019

39

9

5185-5206

10.3934/dcds.2019211

NSFCNational Natural Science Foundation of China (NSFC) [11671092, 11671191, 11871208]; Scientific Research Foundation of Hunan Provincial Education DepartmentHunan Provincial Education Department [16C0763]; Natural Science Foundation of Hunan ProvinceNatural Science Foundation of Hunan Province [2018JJ2159]; Fundamental Research Funds for the Central UniversitiesFundamental Research Funds for the Central Universities [0203-14380022, 0203-14380025]

本校为通讯机构

In this paper, we investigate the dynamics of the following family of rational maps \begin{document}$ \begin{equation*} f_{\lambda}(z) = \frac{z^{2n} - \lambda^{3n+1}}{z^n(z^{2n} - \lambda^{n - 1})} \end{equation*} $\end{document} with one parameter \begin{document}$ \lambda \in \mathbb{C}^* - \{\lambda: \lambda^{2n + 2} = 1\} $\end{document}, where \begin{document}$ n\geq 2 $\end{document}. This family of rational maps is viewed as a singular perturbation of the bi-critical map \begin{document}$ P_{-n}(z) = z^{-n} $\end{document} if \begin{doc...