En búsqueda de dinámicas de aplicaciones en el plano “Iteraciones de funciones reales cuadráticas en el plano”

Abstract

This article shows a classification of quadratic applications in the plane that Guillermo Gomez and Santiago Lopez de Medrano shows in [3] by the conjugation relationship with investable related applications of the plane. And they determined 21 equivalence classes represented by small quadratic applications. This classification gives rise to the study of the dynamics generated by these 21 applications.  

In addition, we will show that a function studied as f () = 2+ is part of the general form of a real quadratic application of the plane itself, and that its dynamics allowed us to know the famous sets of Julia and Fatou , that help us to understand the dynamics of this application and also to enjoy the beauty of the structure of these sets that are part of the fractal sets [4]. For this reason we choose one of the functions as an example, because we want to show how the study of the dynamics can be started. Finally, we will analyze the parameters and constraints that different types of dynamics are determined by the number of fixed points. Likewise, depending on the character of these fixed points, it is possible to predict the dynamics involved. "