MPEJ Volume 4, No.1, 16pp
Received: Dec 3, 1997, Revised: Dec 30, 1997, Accepted: Jan 9, 1998

M. Guzzo, F. Fasso`, G. Benettin
On the Stability of Elliptic Equilibria

ABSTRACT:  We consider stability of elliptic equilibria in Hamiltonian
systems in the frame of Nekhoroshev's theory, recovering the steepness
assumption, in the form of convexity, from an appropriate treatment of
the higher orders. The singularity of the action-angle coordinates is
overcome by using Cartesian coordinates. We introduce an essential
refinement of the perturbative technique used in a previous work on the
subject, and obtain significant improvements of results, namely better
values of the exponents controlling the stability time and the confinement
around equilibrium, in case the equilibrium frequency satisfy stronger
nonresonance conditions. Within the same nonresonance assumptions the
new method provides instead independent informations, namely one gets a
better confinement on a reduced time scale.