Invariant tori in the Sun--Jupiter--Saturn system

Abstract

We discuss the applicability of Kolmogorov's theorem on existence ofinvariant tori to the real Sun-Jupiter-Saturn system. Usingcomputer algebra, we construct a Kolmogorov's normal form defined ina neighborhood of the actual orbit in the phase space, giving asharp evidence of the convergence of the algorithm. If not arigorous proof, we consider our calculation as a strong indicationthat Kolmogorov's theorem applies to the motion of the two biggestplanets of our solar system.