Rational maps whose Julia sets are quasi circles

Q. Al-Salami, Hassanein; Al-shara, Iftichar

doi:10.22075/ijnaa.2021.5341

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	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
تاریخ دریافت: 21 اسفند 1399، تاریخ بازنگری: 06 تیر 1400، تاریخ پذیرش: 18 تیر 1400
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

مراجع
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Rational maps whose Julia sets are quasi circles