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. GiorgilliUltimo
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.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.