FM 00-20 ; mp_arc 00-409

Author: Michele V. Bartuccelli, Guido Gentile

Title: 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, and which leads to a sort of singular implicit function problem. Albeit the solutions are not analytic in the size of the perturbation, an analytic expansion for the solution can be envisaged and successfully used in order to explicitly construct the solution as an absolutely convergent power series.

Keywords: KAM invariant tori, isochronuos systems, perturbation theory, Lindstedt series

Michele Bartuccelli
Department of Mathematics and Statistics,
University of Surrey
Guildford, GU2 7XH
e-mail: m.bartuccelli@eim.surrey.ac.uk

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@matrm3.mat.uniroma3.it