د.عمر اسماعيل الحصادي2024-11-272024-11-27https://dspace.academy.edu.ly/handle/123456789/403All titles that we discussed in this work became easier to understand. In addition, we have shown some figures for more understanding, and we have shown how we can select the Julia set and Fatou set in some examples with figures to show the regions of these sets. Moreover, Some examples have been given to show how we can find the fixed and critical points, and also we view other examples to understand the iteration of rational functions. Also, this work included some theorems with their proof to go deeper and understand some ideas in this work.ABSTRACT The purpose of this study was to shed some light on rational maps. In particular, It aims to study some sets Like Julia's set, and Fatou set, . also to study the rational function, and analytic function with some discussion to understand their properties and their conditions. This research attempted to deal with the Iterations of the polynomial which included some examples of different polynomials. Moreover, the research goes deeper into the study of the Newton’s iteration function.Newton`s Method as an Application of Iteration of Rational Function