{
  "id": "1607.08272",
  "version": "v1",
  "published": "2016-07-27T21:52:42.000Z",
  "updated": "2016-07-27T21:52:42.000Z",
  "title": "Integral points of bounded degree on the projective line and in dynamical orbits",
  "authors": [
    "Joseph Gunther",
    "Wade Hindes"
  ],
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "Let $D$ be a non-empty effective divisor on $\\mathbb{P}^1$. We show that when ordered by height, any set of $(D,S)$-integral points on $\\mathbb{P}^1$ of bounded degree has relative density zero. We then apply this to arithmetic dynamics: let $\\varphi(z)\\in \\overline{\\mathbb{Q}}(z)$ be a rational function of degree at least two whose second iterate $\\varphi^2(z)$ is not a polynomial. We show that as we vary over points $P\\in\\mathbb{P}^1(\\overline{\\mathbb{Q}})$ of bounded degree, the number of algebraic integers in the forward orbit of $P$ is absolutely bounded and zero on average.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-27T21:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "37P15",
      "11G50",
      "11R04",
      "14G05"
    ],
    "keywords": [
      "bounded degree",
      "integral points",
      "projective line",
      "dynamical orbits",
      "non-empty effective divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}