Applicazioni del teorema di Nekhoroshev alla meccanica celeste

Benettin, Giancarlo

Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 71-95 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

The application of Nekhoroshev theory to selected physical systems, interesting for Celestial Mechanics, is here reviewed. Applications include the stability of motions in the weakly perturbed Euler-Poinsot rigid body and the stability of the so-called Lagrangian equilibria $L_{4}$ , $L_{5}$ in the spatial circular restricted three-body problem. The difficulties to be overcome, which require a nontrivial extension of the standard Nekhoroshev theorem, are the presence of singularities in the fiber structure the phase space, and the presence of «degenerate» variables (actions appearing in the perturbation, but not in the unperturbed system).

Publié le : 2001-02-01

MR 1821398 | Zbl 1089.70008

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     author = {Giancarlo Benettin},
     title = {Applicazioni del teorema di Nekhoroshev alla meccanica celeste},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {71-95},
     zbl = {1089.70008},
     mrnumber = {1821398},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_1_71_0}
}

Benettin, Giancarlo. Applicazioni del teorema di Nekhoroshev alla meccanica celeste. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 71-95. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_1_71_0/

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