Applications of the theorem of Nekhoroshev in celestial mechanics (Q2717321)
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scientific article; zbMATH DE number 1604868
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Applications of the theorem of Nekhoroshev in celestial mechanics |
scientific article; zbMATH DE number 1604868 |
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5 January 2004
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Nekhoroshev's theory
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quasi-integrable Hamiltonian
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celestial mechanics
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perturbed Euler-Poinsot rigid body problem
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stability of Lagrangian equilibria
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fiber structure
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phase space
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singularities
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Applications of the theorem of Nekhoroshev in celestial mechanics (English)
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The paper is a survey of new developments (especially obtained by Italian mathematicians) of the well-known Nekhoroshev's theory [\textit{N. N. Nekhoroshev}, Russ. Math. Surv. 32, No. 6, 1-65 (1977; Zbl 0389.70028)]. The theory is applied to the study of dynamical systems important for celestial mechanics. As examples, the author considers the weakly perturbed Euler-Poinsot rigid body problem and the stability of Lagrangian equilibria \(L_4\) and \(L_5\). An important remark is that in all these cases the fiber structure of phase space presents singularities, and thus a carefully geometric study of Hamiltonians is necessary.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00026].
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