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.
Locatelli, U., Giorgilli, A. (2007). Invariant tori in the Sun--Jupiter--Saturn system. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., 7, 377-398.
Invariant tori in the Sun--Jupiter--Saturn system
LOCATELLI, UGO;
2007-01-01
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.File in questo prodotto:
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