{
  "id": "1707.07782",
  "version": "v1",
  "published": "2017-07-25T01:22:11.000Z",
  "updated": "2017-07-25T01:22:11.000Z",
  "title": "A bound for the sum of heights on iterates in terms of a dynamical degree",
  "authors": [
    "Jorge Mello"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.DS"
  ],
  "abstract": "We give a corrected proof for a fact stated on a previous paper by the author, namely, that for any Weil height $h_X$ with respect to an ample divisor on a projective variety $X$, any dynamical system $\\mathcal{F}$ of rational self-maps on $X$, and any $\\epsilon>0$, there is a positive constant $C=C(X, h_X, f, \\epsilon)$ such that $\\sum_{f \\in \\mathcal{F}_n} h^+_X(f(P)) \\leq C. k^n.(\\delta_{\\mathcal{F}} + \\epsilon)^n . h^+_X(P)$ for all points $P$ whose $\\mathcal{F}$-orbit is well defined, with $\\delta_{\\mathcal{F}}$ being a dynamical degree associated with a system of several maps, defined by the author in the previous paper mentioned above.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-25T01:22:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P55",
      "11G50",
      "37P35"
    ],
    "keywords": [
      "dynamical degree",
      "weil height",
      "rational self-maps",
      "ample divisor",
      "corrected proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}