Geodesic
Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class
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
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 659-680 Cet article a éte moissonné depuis la source Numdam

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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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     title = {Uniqueness of invariant {Lagrangian} graphs in a homology or a cohomology class},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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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, Série 5, Tome 8 (2009) no. 4, pp. 659-680. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_659_0/