Dynamical Behavior of some families of cubic functions in complex plane

  • Mizal H. Alobaidi
  • Omar Idan Kadham

Abstract

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function  such that have two critical points  and three fixed points  such that is attracting when  is origin point As shown in figure (2).And  are attracting when  is the region specified by open disc  shown in figure (1.(c)).Second function  such that have two critical points   and three fixed points such that  is attracting when  and that its path is to the origin point as shown in figure (4).And  are attractive when  represents the open disc shown in the figure (3.(c)).Third function  such that  have one critical point  and three fixed points  is attracting that is path is the origin point and  are repelling as shown in figure (5). And all 2-cycles of  are repelling and unstable .


 


http://dx.doi.org/10.25130/tjps.24.2019.139

Published
Dec 22, 2019
How to Cite
ALOBAIDI, Mizal H.; IDAN KADHAM, Omar. Dynamical Behavior of some families of cubic functions in complex plane. Tikrit Journal of Pure Science, [S.l.], v. 24, n. 7, p. 122-128, dec. 2019. ISSN 2415-1726. Available at: <http://tjps.tu.edu.iq/index.php/j/article/view/922>. Date accessed: 22 sep. 2021. doi: http://dx.doi.org/10.25130/j.v24i7.922.
Section
Articles