Transport and stochastic behaviour in the three body problem

In this Master s thesis we study chaos and diffusion in two different problems of celestial mechanics. More concretely, the Sitnikov problem and the restricted planar elliptic three-body problem. The results we present here are not original, we follow the works of Moser and Capinski and Gidea. On the one hand, we see that there exists a topological conjugacy between an extension of the Bernouilli shift and a suitable Poincaré map of the Sitnikov problem, giving rise to the existence of chaotic orbits. On the other hand, we consider the Neptune-Triton system, with their eccentricity as the perturbation parameter and we obtain: the existence of diffusing orbits and a lower bound for the Lebesgue measure of their set, the existence of orbits along which the energy makes chaotic excursions, a lower bound of the Hausdorff dimension for the set of chaotic orbits, and the existence of orbits along which the time evolution of energy approaches a Brownian motion with drift as the perturbation parameter approaches to 0