{
  "id": "0801.3568",
  "version": "v2",
  "published": "2008-01-23T15:28:20.000Z",
  "updated": "2010-12-10T11:30:24.000Z",
  "title": "Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class",
  "authors": [
    "Albert Fathi",
    "Alessandro Giuliani",
    "Alfonso Sorrentino"
  ],
  "comment": "20 pages. Version published on Ann. Sc. Norm. Super. Pisa Cl. Sci.(5) Vol. 8, no. 4, 659-680, 2009",
  "journal": "Ann. Sc. Norm. Super. Pisa Cl. Sci.(5) Vol. 78 (2009), no. 4, 659-680",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.SG"
  ],
  "abstract": "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 $\\rho$. This result extends generically to the $C^0$-closure of KAM tori.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-10T11:30:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J50",
      "37J40"
    ],
    "keywords": [
      "cohomology class",
      "ergodic invariant lagrangian graphs",
      "smooth compact riemannian manifold",
      "result implies global uniqueness",
      "lagrangian kam tori"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3568F"
    }
  }
}