We investigate the long time stability in Nekhoroshev’s sense for the Sun–Jupiter– Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.

Kolmogorov and Nekhoroshev theory for the problem of three bodies / A. Giorgilli, U. Locatelli, M. Sansottera. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 104:1(2009), pp. 159-175. [10.1007/s10569-009-9192-7]

Kolmogorov and Nekhoroshev theory for the problem of three bodies

A. Giorgilli
Primo
;
M. Sansottera
Ultimo
2009

Abstract

We investigate the long time stability in Nekhoroshev’s sense for the Sun–Jupiter– Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.
Exponential stability; KAM theory; Kolmogorov theorem; Nekhoroshev theory; Perturbation theory; Sun-Jupiter-Saturn system
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/61641
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