{
  "id": "0712.0643",
  "version": "v1",
  "published": "2007-12-05T01:15:15.000Z",
  "updated": "2007-12-05T01:15:15.000Z",
  "title": "Free curves and periodic points for torus homeomorphisms",
  "authors": [
    "Alejandro Kocsard",
    "Andres Koropecki"
  ],
  "comment": "to appear in Ergodic Theory and Dynamical Systems",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the relationship between free curves and periodic points for torus homeomorphisms in the homotopy class of the identity. By free curve we mean a homotopically nontrivial simple closed curve that is disjoint from its image. We prove that every rational point in the rotation set is realized by a periodic point provided that there is no free curve and the rotation set has empty interior. This gives a topological version of a theorem of Franks. Using this result, and inspired by a theorem of Guillou, we prove a version of the Poincar\\'e-Birkhoff Theorem for torus homeomorphisms: in the absence of free curves, either there is a fixed point or the rotation set has nonempty interior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-05T01:15:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "37E45"
    ],
    "keywords": [
      "free curve",
      "torus homeomorphisms",
      "periodic point",
      "rotation set",
      "homotopically nontrivial simple closed curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0643K"
    }
  }
}