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

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  • We discuss the applicability of Kolmogorov's theorem on existence of invariant tori to the real Sun-Jupiter-Saturn system. Using computer algebra, we construct a Kolmogorov's normal form defined in a neighborhood of the actual orbit in the phase space, giving a sharp evidence of the convergence of the algorithm. If not a rigorous proof, we consider our calculation as a strong indication that Kolmogorov's theorem applies to the motion of the two biggest planets of our solar system.
    Mathematics Subject Classification: Primary: 70F07; Secondary: 70F10, 37J40, 37N05, 70H08.


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