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_۰\ , I_\infty are quasicircles , we have the family of complex rational maps are given by\begin{equation}\label{e۱}\mathcal{Q}_\alpha(Z)=۲\alpha^{۱-n}\ Z^n -\frac{z^n \left(z^{۲n}-\alpha^{n+۱}\right)}{z^{۲n}-\alpha^{۳n-۱}}, \end{equation}where n\geq ۲ and \alpha \in C\backslash \{۰\}, but \alpha^{۲n-۲}\neq ۱,\;\;\alpha^{۱-n}\neq ۱.

کلیدواژه ها:

Julia Sets ، Fatou Sets ، Singular Perturbation ، Quasi circles