{
  "id": "0904.2719",
  "version": "v1",
  "published": "2009-04-17T15:16:20.000Z",
  "updated": "2009-04-17T15:16:20.000Z",
  "title": "Existence of periodic orbits for geodesible vector fields on closed 3-manifolds",
  "authors": [
    "Ana Rechtman"
  ],
  "journal": "Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1817-1841",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In particular, Reeb vector fields and vector fields that admit a global section are geodesible. We will classify the closed 3-manifolds that admit aperiodic volume preserving real analytic geodesible vector fields, and prove the existence of periodic orbits for real analytic geodesible vector fields (not volume preserving), when the 3-manifold is not a torus bundle over the circle. We will also prove the existence of periodic orbits of C2 geodesible vector fields in some closed 3-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-17T15:16:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbits",
      "real analytic geodesible vector fields",
      "aperiodic volume preserving real",
      "volume preserving real analytic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2719R"
    }
  }
}