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

Ugo Locatelli; Antonio Giorgilli

doi:10.3934/dcdsb.2007.7.377

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2007, Volume 7, Issue 2: 377-398. Doi: 10.3934/dcdsb.2007.7.377

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

Ugo Locatelli^1, and
Antonio Giorgilli^2,

1.
Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma
2.
Università degli Studi di Milano, Via Saldini 50, 20133 Milano

Received: December 31, 2005

Revised: October 31, 2006

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 70F07; Secondary: 70F10, 37J40, 37N05, 70H08.

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