Rational maps whose Julia sets are quasi circles

Abstract

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 bybegin{equation}label{e1}mathcal{Q}_alpha(Z)=2alpha^{1-n} Z^n -frac{z^n left(z^{2n}-alpha^{n+1}right)}{z^{2n}-alpha^{3n-1}}, end{equation}where $ngeq 2$ and $alpha in Cbackslash {0},$ but $alpha^{2n-2}neq 1,;;alpha^{1-n}neq 1.$