Guido Gentile and Giovanni Gallavotti
Degenerate elliptic resonances
(744K, ps)
ABSTRACT. Quasi-periodic motions on invariant tori of an integrable system
of dimension smaller than half the phase space dimension may continue
to exists after small perturbations. The parametric equations of the
invariant tori can often be computed as formal power series in the
perturbation parameter and can be given a meaning via resummations.
Here we prove that, for a class of elliptic tori, a resummation
algorithm can be devised and proved to be convergent, thus extending
to such lower-dimensional invariant tori the methods employed to prove
convergence of the Lindstedt series either for the maximal (i.e. KAM)
tori or for the hyperbolic lower-dimensional invariant tori