Resumen de Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class

Albert Fathi, Alessandro Giuliani, Alfonso Sorrentino

• 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 ρ. This result extends generically to the C0-closure of KAM tori.