Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Julia sets are Cantor circles and Sierpinski carpets for rational maps39373948619310.22075/ijnaa.2022.6193ENHassanein Q.Al-SalamiDepartment of Biology, College of Sciences, University of Babylon, IraqIftichar Al-SharaDepartment of Mathematics, College of Education of Pure Sciences, University of Babylon, IraqJournal Article20210801In this work, we study the family of complex rational maps which is given by<br />$$Q_{\beta }\left(z\right)=2{\beta }^{1-d}z^d-\frac{z^d(z^{2d}-{\beta }^{d+1})}{z^{2d}-{\beta }^{3d-1}},$$<br />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 $. https://ijnaa.semnan.ac.ir/article_6193_2a121c67399d0158d6cf6c6d3e018a23.pdf