Beginnings of a topological classification of the real quadratic applications of the plane part 1

Abstract

The present article aims to illustrate a study method on how to approach topological classifications in the family of real quadratic applications through the classification presented by Guillermo Gómez Alcaraz and López de Medrano. In which the author established a classification by conjugating a family into 21 equivalence classes, where each element of this family belongs to one of these classes.  In addition, the dynamic of any of them is determined by the dynamic of a representative of the class composed with an invertible related application. In other words, to study the dynamics of this last composition, to study the dynamics of real quadratic applications on the plane, and to dramatically reduce the number of parameters to 6. [2] In this first article, we illustrate the study for the class F5 in its first part in which it shows that it is possible to establish first the total number of fixed points that can be found in this family.