{
  "id": "math/9605228",
  "version": "v1",
  "published": "1996-05-07T00:00:00.000Z",
  "updated": "1996-05-07T00:00:00.000Z",
  "title": "The rotation set and periodic points for torus homeomorphisms",
  "authors": [
    "John Franks"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the rotation set $\\rho(F)$ for a lift $F$ of an area preserving homeomorphism $f: \\t^2\\to \\t^2$, which is homotopic to the identity. The relationship between this set and the existence of periodic points for $f$ is least well understood in the case when this set is a line segment. We show that in this case if a vector $v$ lies in $\\rho(F)$ and has both co-ordinates rational, then there is a periodic point $x\\in \\t^2$ with the property that $$\\frac{F^q(x_0)-x_0}q = v$$ where $x_0\\in \\re^2$ is any lift of $x$ and $q$ is the least period of $x$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-05-07T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic point",
      "rotation set",
      "torus homeomorphisms",
      "area preserving homeomorphism",
      "line segment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......5228F"
    }
  }
}