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.

Invariant tori in the Sun-Jupiter Saturn system / U. Locatelli, A. Giorgilli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 7:2(2007), pp. 377-398. [10.3934/dcdsb.2007.7.377]

Invariant tori in the Sun-Jupiter Saturn system

A. Giorgilli
Ultimo
2007

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.
Celestial mechanics; Hamiltonian systems; KAM theory; Perturbation methods; Three-body problem
Settore MAT/07 - Fisica Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/37928
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