{
  "id": "math/0105143",
  "version": "v1",
  "published": "2001-05-17T00:33:25.000Z",
  "updated": "2001-05-17T00:33:25.000Z",
  "title": "Homoclinic classes and finitude of attractors for vector fields on n-manifolds",
  "authors": [
    "C. M. Carballo",
    "C. A. Morales"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "A homoclinic class of a vector field is the closure of the transverse homoclinic orbits associated to a hyperbolic periodic orbit. An attractor (a repeller) is a transitive set to which converges every positive (negative) nearby orbit. We show that a generic C1 vector field on a closed n-manifold has either infinitely many homoclinic classes or a finite collection of attractors (repellers) whose basins form an open-dense set. This result gives an approach to a conjecture by Palis. We also prove the existence of a locally residual subset of C1 vector fields on a 5-manifold having finitely many attractors and repellers but infinitely many homoclinic classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-17T00:33:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C20",
      "37C29"
    ],
    "keywords": [
      "homoclinic classes",
      "n-manifold",
      "generic c1 vector field",
      "hyperbolic periodic orbit",
      "transverse homoclinic orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5143C"
    }
  }
}