{
  "id": "math/0606744",
  "version": "v2",
  "published": "2006-06-29T11:58:58.000Z",
  "updated": "2009-03-11T09:35:46.000Z",
  "title": "Unique Ergodicity of Harmonic Currents on Singular Foliations of P2",
  "authors": [
    "John Erik Fornaess",
    "Nessim Sibony"
  ],
  "comment": "Improved exposition",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let F be a holomorphic foliation of P^2 by Riemann surfaces. Assume all the singular points of F are hyperbolic. If F has no algebraic leaf, then there is a unique positive harmonic $(1,1)$ current $T$ of mass one, directed by F. This implies strong ergodic properties for the foliation. We also study the harmonic flow associated to the current $T.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-11T09:35:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S65",
      "57R30"
    ],
    "keywords": [
      "harmonic currents",
      "singular foliations",
      "unique ergodicity",
      "implies strong ergodic properties",
      "harmonic flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6744F"
    }
  }
}