Dynamical Behavior of some families of cubic functions in complex plane

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 .