Applications of perturbative techniques to the N-body problem
In the 60s V. I. Arnold argued it was possible to apply KAM theory to the N-body problem, in the regime where one mass in much larger then the others, in turn equally sized. His statement, that goes under the name "Theorem of stability of planetary motions" has been completely proved only 50 years later. A key ingredient of the proof was a well pointed system of canonical coordinates which, besides taking into account its nature of close-to-be-integrable system, also was well fitted to its invariance by rotations. I shall describe some applications of the perturbative theory to the N-body problem, trying to highlight the important rôle of the canonical setting in the proofs.