08-18 Albert Fathi, Alessandro Giuliani, Alfonso Sorrentino

Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class. (115K, LATeX 2e) Jan 23, 08

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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.

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