- 96-485 A. Jorba, R. de la Llave, M. Zou
- Lindstedt series for lower dimensional tori.
Oct 9, 96
(auto. generated ps),
of related papers
Abstract. We consider
the perturbative series for lower dimensional tori of nearly integrable
systems on which the motion is conjugate to a Diophantine frequency.
We show that for analytic perturbations there are formal expansions in
all orders of the perturbation. We also prove a KAM type theorem
stating that, under suitable assumptions in the map, given an
approximate parameterization of a lower dimensional torus, it is
possible to find a set of large measure in parameter space where the
torus exists. By combining the two results we obtain that the formal
Lindstedt series define a function except in a small set contained in
a very thin sector. Hence they are Borel summable.