Jorba A., Simo C.
Effective Stability for Periodically Perturbed Hamiltonian Systems.
(23K, Latex)
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.
(This is the text of a paper delivered at the NATO-ASI
"Integrability and chaos in Hamiltonian systems" held
in Torun, Poland 1993)