{
  "id": "1406.3760",
  "version": "v2",
  "published": "2014-06-14T18:27:10.000Z",
  "updated": "2015-11-01T21:42:39.000Z",
  "title": "Spectral flow, crossing forms and homoclinics of Hamiltonian systems",
  "authors": [
    "Nils Waterstraat"
  ],
  "comment": "35 pages; v2: final version, Theorem 2.7 improved according to referee's suggestions, additional minor changes",
  "journal": "Proc. Lond. Math. Soc. (3) 111, 2015, 275-304",
  "categories": [
    "math.DS",
    "math.DG",
    "math.FA",
    "math.SG"
  ],
  "abstract": "We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of nonautonomous Hamiltonian vector fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-14T18:27:10.000Z",
      "comment": "35 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-01T21:42:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J30",
      "37J45",
      "58E07"
    ],
    "keywords": [
      "hamiltonian systems",
      "crossing forms",
      "one-parameter families",
      "deduce sufficient conditions",
      "homoclinic boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3760W"
    }
  }
}