Albert Fathi, Alessandro Giuliani, Alfonso Sorrentino
Uniqueness of Invariant Lagrangian Graphs in a Homology or 
a Cohomology Class.
(115K, LATeX 2e)

ABSTRACT.  Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ 
on the cotangent space $T^*M$, strictly convex and superlinear in the 
momentum variables, we prove uniqueness of certain ergodic invariant 
Lagrangian graphs within a given homology or cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our result implies global uniqueness of Lagrangian KAM tori with rotation vector $\rho$. This result extends generically to the $C^0$-closure of KAM tori.