00-409 Michele V. Bartuccelli, Guido Gentile

Lindstedt series for perturbations of isochronous systems. I. General theory (666K, Postscript) Oct 18, 00

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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. </

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