{
  "id": "1601.03910",
  "version": "v1",
  "published": "2016-01-15T13:28:38.000Z",
  "updated": "2016-01-15T13:28:38.000Z",
  "title": "Growth of the number of periodic points for meromorphic maps",
  "authors": [
    "Tien-Cuong Dinh",
    "Viet-Anh Nguyen",
    "Tuyen Trung Truong"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at most exponentially fast with respect to n and the exponential rate is at most equal to the algebraic entropy of f. Further estimates are given when X is a surface. Among the techniques introduced in this paper, the h-dimension of the density between two arbitrary positive closed currents on a compact Kaehler surface is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-15T13:28:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H50"
    ],
    "keywords": [
      "meromorphic maps",
      "compact kaehler manifold",
      "dominant meromorphic self-map",
      "compact kaehler surface",
      "algebraic entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103910D"
    }
  }
}