Rational maps whose Julia sets are quasi circles

Document Type : Research Paper

Authors

1 Department of Biology, College of Sciences, University of Babylon, Iraq

2 Department of Mathematics, College of Education of Pure Sciences, University of Babylon, Iraq

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 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 $\alpha^{2n-2}\neq 1,\;\;\alpha^{1-n}\neq 1.$

Keywords