{
  "id": "1201.1313",
  "version": "v2",
  "published": "2012-01-05T21:57:46.000Z",
  "updated": "2012-03-08T00:18:03.000Z",
  "title": "Integral points in two-parameter orbits",
  "authors": [
    "Pietro Corvaja",
    "Vijay Sookdeo",
    "Thomas J. Tucker",
    "Umberto Zannier"
  ],
  "comment": "17 pages; minor revisions made",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of degree greater than 1, let S be a finite set of places of K, and suppose that u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively computable. This may be thought of as a two-parameter analog of a result of Silverman on integral points in orbits of rational maps. This issue can be translated in terms of integral points on an open subset of P_1^2; then one can apply a modern version of the method of Runge, after increasing the number of components at infinity by iterating the rational map. Alternatively, an ineffective result comes from a well-known theorem of Vojta.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-08T00:18:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G25",
      "37F10",
      "37P55"
    ],
    "keywords": [
      "integral points",
      "two-parameter orbits",
      "nonconstant rational map",
      "degree greater",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1313C"
    }
  }
}