Lindstedt Series for Lower Dimensional Tori

Lindstedt Series for Lower Dimensional Tori Angel Jorba Rafael De La Llave and Maorong Zou

Degenerate elliptic resonances

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 resumm...

Lindstedt series for perturbations of isochronous systems. I. General theory

Abstract. We give a proof of the persistence of invariant tori for analytic perturbations of isochronous systems by using the Lindstedt series expansion for the solutions. With respect to the case of anisochronous systems, there is the additional problem to find the set of allowed rotation vectors for the invariant tori, which can not given a priori simply by looking at the unperturbed system, ...

Lindstedt Series, Ultraviolet Divergences and Moser's Theorem

Moser's invariant tori for a class of nonanalytic quasi integrable even hamiltonian systems are shown to be analytic in the perturbation parameter. We do so by exhibiting a summation rule for the divergent series (\Lindstedt series") that formally deene them. We nd additional cancellations taking place in the formal series, besides the ones already known and necessary in the analytic case (i.e....

A Possiblemechanism for Thekamtori Breakdown

Inspired by the quantum eld theory, a resummation is performed in the Lindstedt series deening the KAM tori, and a possible mechanism for universality of the tori breakdown is discussed. This work is mostly based on a joint paper with G. Gallavotti.