TITLE: Contribution to the Study of Fourier Methods for Quasi-Periodic Functions and the Vicintiy of the Collinear Libration Points. AUTHOR: J.M. Mondelo (mondelo@ma1.upc.es) Dept. de Matematica Aplicada I, Universitat Politecnica de Catalunya Diagonal, 647, 08028 Barcelona, Spain ABSTRACT: This work is made of two parts. The first one is devoted to the development and study of a procedure for the accurate computation of frequencies and amplitudes of a quasi-periodic function, starting from a set of equally-spaced samples over a finite time interval. Error estimates are developed for the procedure, which are illustrated with numerical examples. The procedure is applied to the developement of simplified models of motion in the Solar System, based on frequency analysis of the numerical JPL ephemeris. The second part is devoted to the study of the neighborhood of the collinear libration points of the Restricted Three-Body problem. The center manifold of these equilibrium points is continued up to where it is computationally feasible, by computing the families of periodic orbits and invariant tori contained in it, using purely numerical procedures. New phenomenology is detected, related to bifurcations of halo-type families of periodic orbits. Due to the large amount of computations required, some algorithms have been parallelized.