TITLE:
Effective computation of the dynamics around a 
two-dimensional torus of a Hamiltonian system.

AUTHORS:
Frederic Gabern and Angel Jorba
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain
E-mails: gabern@mat.ub.es, angel@maia.ub.es

ABSTRACT:
The purpose of this paper is to make an explicit analysis of the
nonlinear dynamics around a two-dimensional invariant torus of an
analytic Hamiltonian system. The study is based on normal form
techniques and the computation of an approximated first integral
around the torus. One of the main novel aspects of the current work is
the implementation of the symplectic reducibility of the
quasi-periodic time-dependent variational equations of the torus. We
illustrate the techniques in a particular example that is a
quasi-periodic perturbation of the well-known Restricted Three Body
Problem. The results are useful to study the neighbourhood of the
triangular points of the Sun-Jupiter system.