Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 4, p. 659-680

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 C 0 -closure of KAM tori.

Classification:  37J50,  37J40,  53D12
@article{ASNSP_2009_5_8_4_659_0,
     author = {Fathi, Albert and Giuliani, Alessandro and Sorrentino, Alfonso},
     title = {Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {4},
     year = {2009},
     pages = {659-680},
     zbl = {1192.37086},
     mrnumber = {2647908},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0}
}
Fathi, Albert; Giuliani, Alessandro; Sorrentino, Alfonso. Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 4, pp. 659-680. http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0/

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