Rational maps whose Julia sets are quasi circles

In this paper, we give a family of rational maps whose Julia sets are quasicircles also we the boundaries of I_0\ , I_\infty are quasicircles , we have the family of complex rational maps are given by\begin{equation}\label{e1}\mathcal{Q}_\alpha(Z)=2\alpha^{1-n}\ Z^n -\frac{z^n \left(z^{2n}-\alpha^{n+1}\right)}{z^{2n}-\alpha^{3n-1}}, \end{equation}where n\geq 2 and \alpha \in C\backslash \{0\}, but \alpha^{2n-2}\neq 1,\;\;\alpha^{1-n}\neq 1.

Rational maps whose Julia sets are quasi circles Keywords:

Julia Sets , Fatou Sets , Singular Perturbation , Quasi circles