01-426 Bambusi D, Gaeta, G.

On persistence of invariant tori and a theorem by Nekhoroshev (53K, LaTeX) Nov 19, 01

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Abstract. We give a proof of a theorem by N.N. Nekhoroshev concerning Hamiltonian systems with $n$ degrees of freedom and $s$ integrals of motion in involution, where $1 \le s \le n$. Such a theorem ensures persistence of $s$-dimensional invariant tori under suitable nondegeneracy conditions generalizing Poincar\'e's condition on the Floquet multipliers. We also deal in detail with perturbations of systems having reducible tori: in this case persistence can be ensured by a nonresonance condition expressed in terms of linear combinations of determinants involving the frequencies of the motion on the torus and the frequencies of small oscillations about the torus

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