{
  "id": "2401.10335",
  "version": "v1",
  "published": "2024-01-18T19:01:38.000Z",
  "updated": "2024-01-18T19:01:38.000Z",
  "title": "A selection principle for a viscosity solution of the Mañé Lagrangian",
  "authors": [
    "Iker Martínez Juárez",
    "Héctor Sánchez Morgado"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a vector field on a compact manifold we consider the invariant measure for the stochastic perturbation as well as the corresponding Ma\\~n\\'e lagrangian. We show that the limit of the invariant measure of the perturbated system, when the perturbation tends to zero, determines a particular weak KAM solution of the lagrangian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-18T19:01:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J50",
      "60F10",
      "49L25"
    ],
    "keywords": [
      "viscosity solution",
      "selection principle",
      "lagrangian",
      "invariant measure",
      "weak kam solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}