{
  "id": "2306.03499",
  "version": "v1",
  "published": "2023-06-06T08:37:33.000Z",
  "updated": "2023-06-06T08:37:33.000Z",
  "title": "Non contractible periodic orbits for generic hamiltonian diffeomorphisms of surfaces",
  "authors": [
    "Patrice Le Calvez",
    "Martin Sambarino"
  ],
  "categories": [
    "math.DS",
    "math.SG"
  ],
  "abstract": "Let $S$ be a closed surface of genus $g\\geq 1$, furnished with an area form $\\omega$. We show that there exists an open and dense set ${\\mathcal O_r}$ of the space of Hamiltonian diffeomorphisms of class $C^r$, $1\\leq r\\leq\\infty$, endowed with the $C^r$-topology, such that every $f\\in \\mathcal O_r$ possesses infinitely many non contractible periodic orbits. We obtain a positive answer to a question asked by Viktor Ginzburg and Ba\\c{s}ak G\\\"{u}rel. The proof is a consequence of recent previous works of the authors [LecSa].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-06T08:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C05",
      "37C20",
      "37C25",
      "37C29",
      "37E30",
      "37E45",
      "37J12"
    ],
    "keywords": [
      "non contractible periodic orbits",
      "generic hamiltonian diffeomorphisms",
      "area form",
      "dense set",
      "viktor ginzburg"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}