{
  "id": "0706.2169",
  "version": "v2",
  "published": "2007-06-14T17:54:02.000Z",
  "updated": "2007-07-08T12:53:58.000Z",
  "title": "Nonarchimedean Green functions and dynamics on projective space",
  "authors": [
    "Shu Kawaguchi",
    "Joseph H. Silverman"
  ],
  "comment": "30 pages. Minor corrections and updated references",
  "journal": "Math. Zeit. 262 (2009), 173--197",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "Let F: P^N_K --> P^N_K be a morphism of degree d > 1 defined over a field K that is algebraically closed and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function G_F associated to F is Holder continuous on P^N(K) and that the Fatou set F is equal to the set of points at which G_F is locally constant. Further, G_F vanishes precisely on the set of points P such that F has good reduction at every point in the forward orbit of P. We also prove that the iterates of F are locally uniformly Lipschitz on the Fatou set of F.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-08T12:53:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32P05",
      "11G25",
      "14G20",
      "32U35",
      "37F10",
      "37F50"
    ],
    "keywords": [
      "nonarchimedean green functions",
      "projective space",
      "fatou set",
      "nonarchimedean absolute value",
      "modified green function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2169K"
    }
  }
}