Benettin, Giancarlo:
Applicazioni del teorema di Nekhoroshev alla meccanica celeste
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.1, p. 71-95, Unione Matematica Italiana (Italian)
pdf (12.43 MB), djvu (364 Kb). | MR1821398 | Zbl 1089.70008
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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).
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