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.

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