{
  "id": "1110.0601",
  "version": "v4",
  "published": "2011-10-04T08:22:49.000Z",
  "updated": "2013-03-13T13:43:15.000Z",
  "title": "Equilibrium measures for the Hénon map at the first bifurcation",
  "authors": [
    "Samuel Senti",
    "Hiroki Takahasi"
  ],
  "comment": "23 pages, 7 figures, former title: The H\\'enon family at the first bifurcation: a thermodynamical study I",
  "journal": "Nonlinearity 26 (2013) 1719-1741",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the dynamics of strongly dissipative H\\'enon maps, at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove the existence of an equilibrium measure which minimizes the free energy associated with the non continuous potential $-t\\log J^u$, where $t\\in\\mathbb R$ is in a certain interval of the form $(-\\infty,t_0)$, $t_0>1$ and $J^u$ denotes the Jacobian in the unstable direction.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-03-13T13:43:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "37G25"
    ],
    "keywords": [
      "equilibrium measure",
      "hénon map",
      "first bifurcation parameter",
      "strongly dissipative henon maps",
      "non continuous potential"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/26/6/1719",
      "journal": "Nonlinearity",
      "year": 2013,
      "month": "Jun",
      "volume": 26,
      "number": 6,
      "pages": 1719
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013Nonli..26.1719S"
    }
  }
}