Browsing by Author "Mengistu, Muluken"

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Iteration of Rational Function, Properties of Faout Sets
    (Addis Ababa University, 2012-01-01) Mengistu, Muluken; Mohammed, Seid (PhD)
    The Central idea of iteration theory is the division of the complex plane in to Fatou set and Julia sets. Especially the paper focuses on properties of Fatou sets of iteration of rational function. We devoted much time on the Fatou and Julia sets due to their particular importance to express properties of Fatou sets. The main objective of this paper is to investigate properties of Fatou sets of iteration of rational function. The paper consists of four main sections: The first section is introductory part, deals with iteration(repeated application) of rational function and some facts on iteration of rational function. In second section, the rational map, conjugacy, valancey, fixed point, Critical point will be defined and discussed; The Extended complex plane, Lipthyz continuous will be defined and elaborated through examples. In the third section, we will come across with equicontinuity and completely invariant sets; not only this formal definition of fatou and Julian sets presented in this section. In last section but the core part of the paper Exceptional points and the back ward orbit will be defined. And then some basic properties of Fatou sets are stated and clarified where the proof of most of these properties are also included. It should be pointed out that these topics are far more in depth than what will be covering here. In fact we can do a whole course on these topics.