{
  "id": "1308.6518",
  "version": "v1",
  "published": "2013-08-29T16:48:16.000Z",
  "updated": "2013-08-29T16:48:16.000Z",
  "title": "Tonelli Lagrangian systems on the 2-torus and topological entropy",
  "authors": [
    "Jan Philipp Schröder"
  ],
  "comment": "38 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study Tonelli Lagrangian systems on the 2-torus in energy levels above Ma\\~n\\'e's strict critical value and analyize the structure of global minimizers in the spirit of Morse, Hedlund and Bangert. In the case where the topological entropy of the Euler-Lagrange flow on the fixed energy level vanishes, we show that there are invariant tori for all rotation vectors indicating integrable-like behavior on a large scale. On the other hand, using a construction of Katok, we give examples of reversible Finsler geodesic flows with vanishing topological entropy, but having ergodic components of positive measure in the unit tangent bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-29T16:48:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological entropy",
      "study tonelli lagrangian systems",
      "rotation vectors indicating integrable-like behavior",
      "unit tangent bundle",
      "fixed energy level vanishes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.6518S"
    }
  }
}