Effective Stability for Periodically Perturbed Hamiltonian Systems

Abstract

In this work we present a method to bound the diffusion near an elliptic equilibrium point of a periodically time-dependent Hamiltonian system. The method is based on the computation of the normal form (up to a certain degree) of that Hamiltonian, in order to obtain an adequate number of (approximate) first integrals of the motion. Then, bounding the variation of those integrals with respect to time provides estimates of the diffusion of the motion.

The example used to illustrate the method is the Elliptic Spatial Restricted Three Body Problem, in a neighbourhood of the points L _4,5. The mass parameter and the eccentricity are the ones corresponding to the Sun-Jupiter case.