Aplicación de la dinámica simbólica en la teoría del caos

Abstract

[en] The aim of this project is to prove the Smale-Birkhoff Theorem, which provides sufficient conditions for a dynamical system to show chaotic behavior. In order to achieve this purpose, it will be apparent that symbolic dynamics play an essential role. This technique consists in characterizing the orbits of a dynamical system with bi-infinite sequences of symbols, so its structure is displayed in a simpler way, while preserving the information concerning to the dynamics. It gives the chance to perform qualitative analysis without the need of manipulating directly the complicated structure that these systems have.