Conjuntos de Julia de una función racional

Abstract

In this work a part of Julia's Joint article of a Rational function (Julia Rational Map Sets) by Linda Keen is developed, a brief analysis of the elements that make up Julia's Sets is made, taking into account its relationship with Functions rational and its properties. This work has been carried out in order to determine the topological properties of this set and try to establish the behavior of the dynamics of these functions. The first chapter introduces some brief ways related to the analysis of the functions of the complex variable, in addition to the basic notions of the theory of work-oriented dynamic systems with rational functions that seek to build the concept of Fatou Set and Julia's set of a rational function. Subsequently, it is sought to characterize the sets of the results from the construction of a series of properties which are used as the moment to identify Julia's set of each of these functions and briefly it is considered a new set which is known as an Exceptional Ensemble that plays an important role when consulting the dynamics of these functions. In addition to this, a relationship between Julia's set and the set of periodic points is evidenced in order to simplify the process of determining Julia's set of a rational function. Finally, describe the behavior of the periodic cycles, specifying an attractive, super-attractor or repellent cycle, characterizing some of its properties.