 01426 Bambusi D, Gaeta, G.
 On persistence of invariant tori and a theorem by Nekhoroshev
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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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