الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Classically, iteration of polynomial and rational maps on or is the topic of discrete complicated dynamic structures. The local theory of analytical iteration dates back to the 19th century, but the modern theory of global complex dynamics begins with the fundamental works of Fatou and Julia. The study of polynomial and rational maps dynamics over and has a lengthy history with many profound theorems. More recently, an analog theory was developed for completed local fields such as p-adic, rational and algebraic closure. The primary goal of this thesis is to study the classification of rational periodic and preperiodic points of cubic polynomials that have coefficients from the rational field. In this thesis we introduced a Complete parametrization of polynomials that has: a) Rational periodic points of exact period .b)Rational preperiodic points of types where .c) Rational preperiodic points of types where .d)Rational preperiodic points of types .e)There is an article obtained from Theorems [3.1.1, 3.1.2, 3.1.6, 3.2.1, 3.2.3, 3.2.5, 3.2.6, 3.2.7, 3.2.8], and this article was accepted to be published in ”Mansoura Journal Of Mathematics”, titled ”On the classification of periodic points of cubic polynomials over Q” with authors ”A.Hashem, M.Sadek and E.Ahmed” This article will appear in Volume 36, No. 1 2019 issue.