{
  "id": "1811.02240",
  "version": "v1",
  "published": "2018-11-06T09:16:37.000Z",
  "updated": "2018-11-06T09:16:37.000Z",
  "title": "Measures of maximal entropy for surface diffeomorphisms",
  "authors": [
    "Jérôme Buzzi",
    "Sylvain Crovisier",
    "Omri Sarig"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that $C^\\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T09:16:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal entropy",
      "generalize smales spectral decomposition theorem",
      "irreducible countable state markov shifts",
      "non-uniformly hyperbolic surface diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}