Kolmogorov and Nekhoroshev theory for the problem of three bodies |
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| Authors: | Antonio Giorgilli Ugo Locatelli Marco Sansottera |
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| Institution: | 1. Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133, Milano, Italy
2. Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133, Rome, Italy
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| 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. |
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