• JIANXUN FU

Articles written in Proceedings – Mathematical Sciences

• Connectivity of the Julia sets of singularly perturbed rational maps

We consider a family of rational functions which is given by

$$f_{\lambda}(z)=\frac{z^n(z^{2n}-\lambda^{n+1})}{z^{2n}-\lambda^{3n-1}},$$

where $n\geq 2$ and $\lambda\in\mathbb{C}^{*}-\{\lambda:\lambda^{2n-2}=1\}$.When $\lambda\neq 0$ is small, $f_{\lambda}$ can be seen as a perturbation of the unicritical polynomial $z\mapsto z^{n}$. It was known that in this case the Julia set $J(f_\lambda)$ of $f_\lambda$ is a Cantor set of circles on which the dynamics of $f_\lambda$ is not topologically conjugate to that of any McMullen maps. In this paper, we prove that this is the unique case such that $J(f_\lambda)$ is disconnected.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019