{
  "id": "1901.01533",
  "version": "v1",
  "published": "2019-01-06T12:22:34.000Z",
  "updated": "2019-01-06T12:22:34.000Z",
  "title": "Periodic orbits of large diameter for circle maps",
  "authors": [
    "Lluís Alsedà",
    "Sylvie Ruette"
  ],
  "comment": "Published in 2010 (published paper freely avaibable on AMS website)",
  "journal": "Proceedings of the American Mathematical Society, 138, No 9, 3211-3217, 2010",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be a continuous circle map and let $F$ be a lifting of $f$. In this note we study how the existence of a large orbit for $F$ affects its set of periods. More precisely, we show that, if $F$ is of degree $d\\geq 1$ and has a periodic orbit of diameter larger than 1, then $F$ has periodic points of period $n$ for all integers $n\\geq 1$, and thus so has $f$. We also give examples showing that this result does not hold when the degree is non positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-06T12:22:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E15"
    ],
    "keywords": [
      "periodic orbit",
      "large diameter",
      "continuous circle map",
      "diameter larger",
      "periodic points"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}