{
  "id": "1605.00258",
  "version": "v1",
  "published": "2016-05-01T14:25:27.000Z",
  "updated": "2016-05-01T14:25:27.000Z",
  "title": "Lecture notes on closed orbits for twisted autonomous Tonelli Lagrangian flows",
  "authors": [
    "Gabriele Benedetti"
  ],
  "comment": "One figure. To appear in a special issue of \"Publicaciones Matem\\'aticas del Uruguay\" dedicated to Ricardo Ma\\~n\\'e. Comments are welcome",
  "categories": [
    "math.DS",
    "math.SG"
  ],
  "abstract": "These notes were prepared in occasion of a mini-course given by the author at the \"CIMPA Research School - Hamiltonian and Lagrangian Dynamics\" (10-19 March 2015 - Salto, Uruguay). The talks were meant as an introduction to the problem of finding periodic orbits of prescribed energy for autonomous Tonelli Lagrangian systems on the twisted cotangent bundle of a closed manifold. In the first part of the lecture notes, we put together in a general theorem old and new results on the subject. In the second part, we focus on an important class of examples: magnetic flows on surfaces. For such systems, we discuss a special method, originally due to Taimanov, to find periodic orbits with low energy and we study in detail the stability properties of the energy levels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-01T14:25:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J45",
      "58E05"
    ],
    "keywords": [
      "twisted autonomous tonelli lagrangian flows",
      "lecture notes",
      "closed orbits",
      "periodic orbits",
      "autonomous tonelli lagrangian systems"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}