  The manifold M being compact and connected and H being a Tonelli Hamiltonian
such that the cotangent bundle of M is equal to the dual tiered Mane set, we
prove that there is a partition of the cotangent bundle of M into invariant C0
Lagrangian graphs. Moreover, among these graphs, those that are C1 cover a
residual subset of this cotangent bundle The dynamic restricted to each of
these sets is non wandering.
