A KAM theorem for finitely differentiable Hamiltonian systems
Abstract Given l 2 n 2 d 4 we prove the persistence of a Cantor family of KAM tori of measure O e 1 2 n l for any non degenerate nearly integrable Hamiltonian system of class C l D x T d where n 1 is the Diophantine power of the frequencies of the persistent KAM tori and D R d is a bounded domain, provided that the size e of the perturbation is sufficiently small. This extends a result by D. Salamon in [25] according to which we do have the persistence of a single KAM torus in the same framework. Moreover, as for the persistence of a single torus, the regularity assumption is essentially optimal.