{
  "id": "0706.2297",
  "version": "v1",
  "published": "2007-06-15T13:52:02.000Z",
  "updated": "2007-06-15T13:52:02.000Z",
  "title": "The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem",
  "authors": [
    "Bau-Sen Du"
  ],
  "comment": "11 pages",
  "journal": "Bull. Austral. Math. Soc. 31(1985), 89-103. Corrigendum: 32 (1985), 159",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "Let f(x) be a continuous function from a compact real interval into itself with a periodic orbit of minimal period m, where m is not an integral power of 2. Then, by Sharkovsky's theorem, for every positive integer n with m \\prec n in the Sharkovsky's ordering defined below, a lower bound on the number of periodic orbits of f(x) with minimal period n is 1. Could we improve this lower bound from 1 to some larger number? In this paper, we give a complete answer to this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-15T13:52:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "37C25",
      "37E15"
    ],
    "keywords": [
      "periodic orbit",
      "sharkovskiis theorem",
      "minimal number",
      "minimal period"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2297D"
    }
  }
}