{
  "id": "1201.1027",
  "version": "v2",
  "published": "2012-01-04T22:27:43.000Z",
  "updated": "2012-07-28T15:32:21.000Z",
  "title": "On periodic solutions of 2-periodic Lyness difference equations",
  "authors": [
    "Guy Bastien",
    "Victor Mañosa",
    "Marc Rogalski"
  ],
  "comment": "27 pages; 1 figure",
  "journal": "Int. J. Bifurcations and Chaos. 23, 4 (2013), 1350071 (18 pages)",
  "doi": "10.1142/S0218127413500715",
  "categories": [
    "math.DS",
    "math.AG",
    "nlin.SI"
  ],
  "abstract": "We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-28T15:32:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A20",
      "39A11"
    ],
    "keywords": [
      "lyness difference equations",
      "periodic solutions",
      "recurrence",
      "initial conditions giving rise",
      "positive initial conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "International Journal of Bifurcation and Chaos",
      "year": 2013,
      "month": "Apr",
      "volume": 23,
      "number": 4,
      "pages": 1350071
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013IJBC...2350071B"
    }
  }
}