{
  "id": "1209.2224",
  "version": "v2",
  "published": "2012-09-11T05:38:21.000Z",
  "updated": "2014-05-18T10:11:33.000Z",
  "title": "Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties",
  "authors": [
    "Samuel Senti",
    "Hiroki Takahasi"
  ],
  "comment": "39 pages, 8 figures. Ergodic Theory and Dynamical Systems, to appear",
  "categories": [
    "math.DS"
  ],
  "abstract": "For strongly dissipative H\\'enon maps at the first bifurcation where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e., prove the existence and uniqueness of an invariant probability measure which maximizes the free energy associated with a non continuous geometric potential $-t\\log J^u$, where $t\\in\\mathbb R$ is in a certain large interval and $J^u$ is the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-18T10:11:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37D45"
    ],
    "keywords": [
      "first bifurcation",
      "equilibrium measures",
      "hénon map",
      "geometric/statistical properties",
      "uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2224S"
    }
  }
}