KAM theory in configuration space

A new approach to the Kolmogorov-Arnold-Moser theory concermng the existence of invariant ton having prescnbed frequencies îs presented It îs based on the Lagrangian formahsm m configuration space instead of the Hamiltonian formahsm in phase space used in earher approaches In particular, the construction of the invariant ton avoids the composition of infinitely many coordinate transformations The regulanty results obtained are apphed to invariant curves of monotone twist maps The Lagrangian approach has been prompted by a récent study of minimal foliations for vanational problems on a torus by J Moser