96-485 A. Jorba, R. de la Llave, M. Zou

Lindstedt series for lower dimensional tori. (138K, Latex) Oct 9, 96

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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.

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