Introducción a la teoría de los sistemas dinámicos

Abstract

Dynamical Systems is a branch of mathematics that studies the behavior of systems evolving over time according to specific rules or laws. Its applications span various fields: in physics, it is used to study deterministic chaos and celestial mechanics; in biology, it helps model population growth and the spread of diseases; in economics, it analyzes business cycles and market dynamics, among others. However, the complexity and abstract nature of this theory often reserve its study for postgraduate students. Therefore, the purpose of this work is to design a document on Dynamical Systems Theory aimed at enabling undergraduate students to begin exploring this subject during their academic training. A qualitative research approach with a descriptive scope and documentary design was used to achieve this goal. The primary result of the study was the creation of a reference document that introduces the foundations of this theory in detail. The document includes definitions accompanied by illustrative examples, theorems with their respective demonstrations, graphical representations, and other essential elements to enhance understanding. Specifically, it delves into topics such as hyperbolicity, symbolic dynamics, topological conjugacy, and chaos. In conclusion, this project provides a solid foundation in Dynamical Systems Theory for undergraduate students. Furthermore, it can serve as a starting point for postgraduate studies, such as master’s and doctoral programs, as well as future research in pure and applied mathematics.