Abstract:

\nIn the 60s V. I. Arnold argued it was possib
le to apply KAM theory to the N-body problem\, in the regime where one mas
s in much larger then the others\, in turn equally sized. His statement\,
that goes under the name "Theorem of stability of planetary motions" has b
een completely proved only 50 years later. A key ingredient of the proof w
as a well pointed system of canonical coordinates which\, besides taking i
nto account its nature of close-to-be-integrable system\, also was well fi
tted 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.