KAM THEORY NEAR MULTIPLICITY ONE RESONANT SURFACES IN PERTURBATIONS OF A-PRIORI STABLE HAMILTONIAN-SYSTEMS

We consider a near-integrable Hamiltonian system in the action-angle v ariables with analytic Hamiltonian. For a given resonant surface of mu ltiplicity one we show that near a Canter set of points on this surfac e, whose remaining frequencies enjoy the usual diophantine condition, the Hamiltonian may be written in a simple normal form which, under ce rtain assumptions, may be related to the class which, following Chierc hia and Gallavotti [1994], we call a-priori unstable. For the a-priori unstable Hamiltonian we prove a KAM-type result for the survival of w hiskered tori under the perturbation as an infinitely differentiable f amily, in the sense of Whitney, which can then be applied to the above normal form in the neighborhood of the resonant surface.