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.

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
Fathi, Albert 1; Giuliani, Alessandro 2; Sorrentino, Alfonso 3, 4

1 Ecole Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, UMR CNRS 5669, 46 allée d’Italie, 69364 Lyon Cedex 07, France
2 Dipartimento di Matematica, Università degli Studi di Roma Tre, L.go S. Leonardo Murialdo 1, 00146 Roma, Italia
3 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000, USA
4 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wiberforce Road, Cambridge CB3 OWB, UK
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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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