FM: 04-06; mp_arc 159; math.DS/0405420

Authors : G.Gentile and G. Gallavotti

Title: Degenerate elliptic resonances

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

Keywords: KAM theory, Divergent Series, Lindstedt Series, Lower-dimensional ellipric tory, Degeneracy, Resummations, Renormalization Group, Quantum Field Theory

Giovanni Gallavotti
Dipartimento di Fisica, Università di Roma ``La Sapienza"
P.le Moro 2
00185 Roma, Italia
tel +39-06-4991-4370
fax +39-06-4957697

Guido Gentile
Dipartimento di Matematica, Università di Roma Tre
L. S. Leonardo Murialdo
00100 Roma, Italia
tel +39-06-54-888-226