American Institute of Mathematical Sciences

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March  2007, 7(2): 377-398. doi: 10.3934/dcdsb.2007.7.377

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, Italy
2. 

Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

Received  January 2006 Revised  November 2006 Published  December 2006

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.
Keywords: Celestial echanics., Hamiltonian systems, Three--body problem, perturbation methods, KAM theory.
Mathematics Subject Classification: Primary: 70F07; Secondary: 70F10, 37J40, 37N05, 70H0.
Citation: Ugo Locatelli, Antonio Giorgilli. Invariant tori in the Sun--Jupiter--Saturn system. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 377-398. doi: 10.3934/dcdsb.2007.7.377
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