{
  "id": "1901.09406",
  "version": "v1",
  "published": "2019-01-27T17:05:18.000Z",
  "updated": "2019-01-27T17:05:18.000Z",
  "title": "Multiple periodic solutions for one-sided sublinear systems: A refinement of the Poincaré-Birkhoff approach",
  "authors": [
    "Tobia Dondè",
    "Fabio Zanolin"
  ],
  "comment": "35 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we prove the existence of multiple periodic solutions (harmonic and subharmonic) for a class of planar Hamiltonian systems which include the case of the second order scalar ODE $x'' + a(t)g(x) = 0$ with $g$ satisfying a one-sided condition of sublinear type. We consider the classical approach based on the Poincar\\'{e}-Birkhoff fixed point theorem as well as some refinements on the side of the theory of bend-twist maps and topological horseshoes. The case of complex dynamics is investigated, too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-27T17:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C25",
      "34C28",
      "54H20"
    ],
    "keywords": [
      "multiple periodic solutions",
      "one-sided sublinear systems",
      "poincaré-birkhoff approach",
      "refinement",
      "second order scalar ode"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}