{
  "id": "math/0108226",
  "version": "v1",
  "published": "2001-08-31T19:07:32.000Z",
  "updated": "2001-08-31T19:07:32.000Z",
  "title": "Homoclinic classes for generic C^1 vector fields",
  "authors": [
    "C. M. Carballo",
    "C. A. Morales",
    "M. J. Pacifico"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that homoclinic classes for a residual set of C^1 vector fields X on closed n-manifolds are maximal transitive and depend continuously on periodic orbit data. In addition, X does not exhibit cycles formed by homoclinic classes. We also prove that a homoclinic class of X is isolated if and only if it is Omega-isolated, and that it is the intersection of its stable set and its unstable set. All these properties are well known for structurally stable Axiom A vector fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-08-31T19:07:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C20",
      "37C29"
    ],
    "keywords": [
      "vector fields",
      "homoclinic classes",
      "periodic orbit data",
      "residual set",
      "closed n-manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......8226C"
    }
  }
}