On a rigorous proof of the KAM stability for the secular
part of the three-body planetary problem:
the Sun-Jupiter-Saturn system
U. Locatelli
University of Milano,
Italy
Abstract: The very classical problem of the three-body planetary
system is revisited into the light of the KAM theory.
The following points will be discussed:
a) introduction of our model (including some terms of order two
with respect to the masses) of the secular Hamiltonian;
b) the Kolmogorov's normalization algorithm as an effective
method to approximate the trajectories in the secular
Hamiltonian of the three-body problem;
c) short description of a computer-assisted proof on the existence of the
invariant tori which is based on the Kolmogorov's normalization algorithm;
d) application of the latter computer-assisted proof on the secular part
of the Sun-Jupiter-Saturn system in order to ensure its stability;
e) how the model introduced at point a) can be improved?
Sketch of a possibly effective extension of the Kolmogorov's algorithm
to the construction of the invariant tori in the complete three-body
problem.