{
  "id": "1901.01524",
  "version": "v1",
  "published": "2019-01-06T10:06:34.000Z",
  "updated": "2019-01-06T10:06:34.000Z",
  "title": "Rotation sets for graph maps of degree 1",
  "authors": [
    "Lluís Alsedà",
    "Sylvie Ruette"
  ],
  "comment": "Published in 2008 (freely available on the website of Annales de l'Institut Fourier)",
  "journal": "Annales de l'Institut Fourier, 58, No. 4, 1233-1294, 2008",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a continuous map on a topological graph containing a loop $S$ it is possible to define the degree (with respect to the loop $S$) and, for a map of degree $1$, rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop $S$ then the set of rotation numbers of points in $S$ has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational $\\alpha$ in this interval there exists a periodic point of rotation number $\\alpha$. For a special class of maps called combed maps, the rotation set displays the same nice properties as the continuous degree one circle maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-06T10:06:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E45",
      "37E25",
      "54H20",
      "37E15"
    ],
    "keywords": [
      "rotation number",
      "graph maps",
      "periodic point",
      "circle map",
      "rotation set displays"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}