Estimates on Invariant Tori Near an Elliptic Equilibrium Point of a Hamiltonian System

We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilibrium point of a Hamiltonian system. If the frequencies of the elliptic point are nonresonant up to a certain order K 4, and a nondegeneracy condition is fulfilled, we get an estimate for the measure of the complement of the KAM tori in a neighbourhood of given radius. Moreover, if the frequencies satisfy a Diophantine condition, with exponent ø , we show that in a neighbourhood of radius r the measure of the...