{
  "id": "1808.02849",
  "version": "v1",
  "published": "2018-08-08T16:26:38.000Z",
  "updated": "2018-08-08T16:26:38.000Z",
  "title": "A Gap Principle for Subvarieties with Finitely Many Periodic Points",
  "authors": [
    "Keping Huang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "Let $f:X\\rightarrow X$ be a quasi-finite endomorphism of an algebraic variety $X$ defined over a number field $K$ and fix an initial point $a\\in X$. We consider a special case of the dynamical Mordell-Lang Conjecture, where the subvariety $V$ contains only finitely many periodic points and does not contain any positive-dimensional periodic subvariety. We show that the set $\\{n\\in \\mathbb{N}~|~f^n(a) \\in V \\}$ satisfies a strong gap principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-08T16:26:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic points",
      "positive-dimensional periodic subvariety",
      "strong gap principle",
      "algebraic variety",
      "initial point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}