{
  "id": "1108.2899",
  "version": "v3",
  "published": "2011-08-14T18:59:13.000Z",
  "updated": "2012-04-25T19:19:27.000Z",
  "title": "Periods of orbits for maps on graphs homotopic to a constant map",
  "authors": [
    "Chris Bernhardt",
    "Zach Gaslowitz",
    "Adriana Johnson",
    "Whitney Radil"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point with period $2^k$. The second is that if $v=2^ks$ for odd $s>1$, then for all $r>s$ there exists a periodic point of minimum period $2^k r$. These results are then compared to the Sharkovsky ordering of the positive integers. (The final version of this paper will appear in the Journal of Difference Equations and Applications.)",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-04-25T19:19:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E15",
      "37E25",
      "37E45"
    ],
    "keywords": [
      "constant map",
      "graphs homotopic",
      "periodic point",
      "periodic orbit",
      "vertices form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2899B"
    }
  }
}