{
  "id": "1905.06202",
  "version": "v1",
  "published": "2019-05-15T14:16:53.000Z",
  "updated": "2019-05-15T14:16:53.000Z",
  "title": "Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states",
  "authors": [
    "Renaud Leplaideur"
  ],
  "comment": "43 pages 14 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any 3-dimensional singular hyperbolic attractor admits for any H\\\"older continuous potential $V$ at most one equilibrium state for $V$ among regular measures. We give a condition on $V$ which ensures that no singularity can be an equilibrium state. Thus, for these $V$'s, there exists a unique equilibrium state and it is a regular measure. Applying this for $V\\equiv 0$, we show that any 3-dimensional singular hyperbolic attractor admits a unique measure of maximal entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-15T14:16:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular hyperbolic flows",
      "maximal entropy",
      "singular hyperbolic attractor admits",
      "regular measure",
      "uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}