The Poincaré-Lyapounov-Nekhoroshev Theorem |
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Authors: | Giuseppe Gaeta |
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Institution: | Dipartimento di Matematica, Università di Milano, via Saldini 50, Milan, I-20133, Italy Dipartimento di Fisica, Università di Roma, p.le A. Moro 2, Rome, I-00185, Italy |
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Abstract: | We give a detailed and mainly geometric proof of a theorem by N. N. Nekhoroshev for hamiltonian systems in n degrees of freedom with k constants of motion in involution, where 1≤k≤n. This state's persistence of k-dimensional invariant tori, and local existence of partial action-angle coordinates, under suitable nondegeneracy conditions. Thus it admits as special cases the Poincaré-Lyapounov theorem (corresponding to k=1) and the Liouville-Arnold one (corresponding to k=n) and interpolates between them. The crucial tool for the proof is a generalization of the Poincaré map, also introduced by Nekhoroshev. |
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