Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class

• Albert Fathi ^[1] ; Alessandro Giuliani ^[3] ; Alfonso Sorrentino ^[2]
  1. [1] École Normale Supérieure de Lyon

     École Normale Supérieure de Lyon

     Arrondissement de Lyon, Francia

     
  2. [2] Princeton University

     Princeton University

     Estados Unidos

     
  3. [3] Università degli Studi di Roma Tre

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 8, Nº 4, 2009, págs. 659-680
• Idioma: inglés
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• Resumen

  • 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 C0-closure of KAM tori.