{
  "id": "1210.6246",
  "version": "v3",
  "published": "2012-10-23T14:27:52.000Z",
  "updated": "2013-07-03T13:13:48.000Z",
  "title": "Determination of all rational preperiodic points for morphisms of PN",
  "authors": [
    "Benjamin Hutz"
  ],
  "comment": "18 pages. To appear in Mathematics of Computation. Sage implementation of the algorithm is Sage Trac Ticket #14219",
  "categories": [
    "math.NT"
  ],
  "abstract": "For a morphism $f:\\P^N \\to \\P^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number field $K$. This algorithm is implemented in the open-source software Sage for $\\Q$. Additionally, the notion of a dynatomic zero-cycle is generalized to preperiodic points. Along with examining their basic properties, these generalized dynatomic cycles are shown to be effective.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-03T13:13:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P05",
      "37P15",
      "37-04"
    ],
    "keywords": [
      "rational preperiodic points",
      "determination",
      "open-source software sage",
      "dynatomic zero-cycle",
      "basic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6246H"
    }
  }
}