- 00-409 Michele V. Bartuccelli, Guido Gentile
- Lindstedt series for perturbations
of isochronous systems. I. General theory
Oct 18, 00
(auto. generated ps),
of related papers
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.