Invariant tori in the secular
motions of the three-body planetary systems

by Ugo Locatelli and Antonio Giorgilli

**Abstract:**
We consider the problem of the applicability of KAM
theorem to a realistic problem of three bodies. In the framework of
the averaged dynamics over the fast angles for the Sun--Jupiter--Saturn
system we can prove the perpetual stability of the orbit. The proof
is based on semi--numerical algorithms requiring both explicit algebraic
manipulations of series and analytical estimates. The proof is made
rigorous by using interval arithmetics in order to control the
numerical errors.

G-zipped file;
Zip compressed file;