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Julia sets are Cantor circles and Sierpinski carpets for rational maps | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3937-3948 اصل مقاله (668.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6193 | ||
| 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: 10 مرداد 1400، تاریخ بازنگری: 13 شهریور 1400، تاریخ پذیرش: 23 مهر 1400 | ||
| چکیده | ||
| In this work, we study the family of complex rational maps which is given by $$Q_{\beta }\left(z\right)=2{\beta }^{1-d}z^d-\frac{z^d(z^{2d}-{\beta }^{d+1})}{z^{2d}-{\beta }^{3d-1}},$$ where $d$ greater than or equal to 2 and $\beta{\in }\mathbb{C}{\backslash }\{0\}$ such that $\beta^{1-d}\ne 1$ and $\beta^{2d-2}\ne 1$. We show that ${J(Q}_\beta$) is a Cantor circle or a Sierpinski carpet or a degenerate Sierpinski carpet, whenever the image of one of the free critical points for $Q_\beta$ is not converge to $0$ or $\infty $. | ||
| کلیدواژه‌ها | ||
| Julia sets؛ Cantor circle؛ Sierpinski carpet؛ degenerate Sierpinski carpet | ||
| مراجع | ||
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