@article {
author = {Al-Salami, Hassanein and Al-Shara, Iftichar},
title = {Julia sets are Cantor circles and Sierpinski carpets for rational maps},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {1},
pages = {3937-3948},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2022.6193},
abstract = {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 $. },
keywords = {Julia Sets,Cantor circle,Sierpinski carpet,degenerate Sierpinski carpet},
url = {https://ijnaa.semnan.ac.ir/article_6193.html},
eprint = {https://ijnaa.semnan.ac.ir/article_6193_2a121c67399d0158d6cf6c6d3e018a23.pdf}
}