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.