On the existence and geometry of invariant tori in the method of averaging

Summary In this paper some results on the Method of Averaging are presented. We give new conditions for the existence of attractive invariant tori together with some information on their domain of attraction. The results are based on invariant manifold theory and error estimation. An application to the rotational motion of Mercury is given.Dedicated to Professor Hans-Wilhelm Knobloch on the Occasion of his 60th Anniversary