Rational maps whose Julia sets are quasi circles

	Rational maps whose Julia sets are quasi circles
International Journal of Nonlinear Analysis and Applications
دوره 12، شماره 2، بهمن 2021، صفحه 2041-2048 اصل مقاله (470.47 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5341
نویسندگان
Hassanein Q. Al-Salami^* ¹؛ Iftichar Al-shara²
¹Department of Biology, College of Sciences, University of Babylon, Iraq
²Department of Mathematics, College of Education of Pure Sciences, University of Babylon, Iraq
چکیده
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 $\alpha^{2n-2}\neq 1,\;\;\alpha^{1-n}\neq 1.$
کلیدواژه‌ها
Julia Sets؛ Fatou Sets؛ Singular Perturbation؛ Quasi circles
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