Different dynamical aspects of Lorenz system

Abstract

[en] This work is focused on describing the most important properties of the skeleton of the phase space, the Lorenz attractor and the parameter space to understand the Lorenz system. We use different methods to describe the Lorenz system, which includes analytical and numerical tools. Firstly, we summarize some properties and basic concepts of the system, in particular, we study stationary points, bifurcations, invariant manifolds and homoclinic and periodic orbits. Moreover, a description of the geometrical model of the Lorenz attractor is given. Based on this model, we analyse the dynamics of the attractor. We discuss how the strong stable foliation formalizes the numerical evidences obtained previously in different simulations. The existence of this foliation was done through a computer assisted proof, and we also present the main steps of this proof. Finally, this work explores the parameter space using ideas of Kneading theory.