{
  "id": "math/9301220",
  "version": "v1",
  "published": "1993-01-23T00:00:00.000Z",
  "updated": "1993-01-23T00:00:00.000Z",
  "title": "Distribution of periodic points of polynomial diffeomorphisms of C^2",
  "authors": [
    "Eric Bedford",
    "Mikhail Lyubich",
    "John Smillie"
  ],
  "doi": "10.1007/BF01232671",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\\C^2$: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure $\\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\\mu$ as the limit distribution of the periodic points of $f$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-01-23T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic points",
      "polynomial diffeomorphisms",
      "equilibrium measure",
      "unique measure",
      "limit distribution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Inventiones Mathematicae",
      "year": 1993,
      "volume": 114,
      "pages": 277
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993InMat.114..277B"
    }
  }
}