Abstract:

\nIn t
he 60s V. I. Arnold argued it was possible to apply KAM theory to the N-bo
dy 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 year
s later. A key ingredient of the proof was a well pointed system of canoni
cal coordinates which\, besides taking into account its nature of close-to
-be-integrable system\, also was well fitted to its invariance by rotation
s. 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.