{
  "id": "1810.03841",
  "version": "v1",
  "published": "2018-10-09T07:57:00.000Z",
  "updated": "2018-10-09T07:57:00.000Z",
  "title": "Heights and periodic points for one-parameter families of Hénon maps",
  "authors": [
    "Liang-Chung Hsia",
    "Shu Kawaguchi"
  ],
  "comment": "40 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "In this paper we study arithmetic properties of a one-parameter family ${\\mathbf H}$ of H\\'enon maps over the affine line. Given a family of initial points ${\\mathbf P}$ satisfying a natural condition, we show the height function $h_{{\\mathbf P}}$ associated to ${\\mathbf H}$ and ${\\mathbf P}$ is the restriction of the height function associated to a semipositive adelically metrized line bundle on projective line. We then show various local properties of $h_{{\\mathbf P}}$. Next we consider the set $\\Sigma({\\mathbf P})$ consisting of periodic parameter values, and study when $\\Sigma({\\mathbf P})$ is an infinite set or not. We also study unlikely intersections of periodic parameter values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T07:57:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic points",
      "hénon maps",
      "one-parameter family",
      "periodic parameter values",
      "height function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}