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Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class. (English) Zbl 1192.37086

In the framework of Hamiltonian systems on the cotangent bundle of a compact manifold it is proved the uniqueness of certain ergodic invariant Lagrangian graphs within a given homology or cohomology class. For quasi-integrable Hamiltonian systems, this implies the global uniqueness of Lagrangian KAM tori with given rotation vector.

MSC:

37J50 Action-minimizing orbits and measures (MSC2010)
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
53D12 Lagrangian submanifolds; Maslov index
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