Title of article :
Julia sets are Cantor circles and Sierpinski carpets for rational maps
Author/Authors :
Q. Al-Salami, Hassanein Department of Biology - College of Sciences - University of Babylon, Iraq , Al-Shara, Iftichar Department of Mathematics - College of Education of Pure Sciences - University of Babylon, Iraq
Abstract :
In this work, we study the family of complex rational maps which is given by
Qβ(z)=2β1−dzd−zd(z2d−βd+1)z2d−β3d−1,
where d greater than or equal to 2 and β∈C∖{0} such that β1−d≠1 and β2d−2≠1. We show that J(Qβ) is a Cantor circle or a Sierpinski carpet or a degenerate Sierpinski carpet, whenever the image of one of the free critical points for Qβ is not converge to 0 or ∞.
Keywords :
Julia sets , Cantor circle , Sierpinski carpet , degenerate Sierpinski carpet
Journal title :
International Journal of Nonlinear Analysis and Applications
