How to apply numerical tools to study dynamical systems : The CP problem

Abstract

Given a system of differential equations, normally it is not possible to find the associated solutions analytically, so other ways have to be taken into account in order to describe the behaviour of the system. The goal of this thesis is to study how to construct numerically the skeleton of a given dynamical system, starting with the computation of the easiest solutions -equilibrium points- and following with other invariant objects as manifolds of equilibria, homoclinic orbits, periodic orbits (PO), manifolds of PO, chaos, island chains, etc. Thanks to these particular solutions and using well-known theory of Dynamical Systems, one can get an idea of the general behaviour of the system. The project studies the particular case of the system that models the behaviour of a hydrogen atom in a circularly polarized microwave field (CP problem).