Dinàmica simbòlica i aplicacions als sistemes dinàmics

Abstract

[en] Chaos theory is a branch of mathematics focusing on dynamic systems with irregular behavior. Despite being deterministic dynamical systems, their behavior cannot be predicted since small differences in initial conditions can cause the system to evolve very differently. In this paper we will see some examples of very simple dynamical systems but with chaotic dynamics. We will focus mainly on the study of the family $Q_{c}(x)=x^{2}+c$ on the real and complex case. We will talk about symbolic dynamics and topological conjugacy as a useful tool to compare dynamical systems and transfer information from one to another. These two concepts will be used to prove that a dynamical system is chaotic.