EXISTENCE OF KAM TORI IN DEGENERATE HAMILTONIAN-SYSTEMS

This article is devoted to the proof that invariant tori still exist i n perturbed integrable Hamiltonian systems with n degrees of freedom H (p, q) = N(p)+P(p, q) if the hypothesis of nondegeneracy is replaced b y a much weaker one that the rank of the mapping theta N/theta p can b e any positive integer smaller than n provided the image of any open s et under the mapping includes a C-n+2 curved one-dimensional submanifo ld. (C) 1994 Academic Press, Inc.