{
  "id": "1011.3546",
  "version": "v1",
  "published": "2010-11-15T23:01:22.000Z",
  "updated": "2010-11-15T23:01:22.000Z",
  "title": "Shadowing, expansiveness and stability of divergence-free vector fields",
  "authors": [
    "Célia Ferreira"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: 1. X is in the C1-interior of the set of expansive divergence-free vector fields. 2. X is in the C1-interior of the set of divergence-free vector fields which satisfy the shadowing property. 3. X is in the C1-interior of the set of divergence-free vector fields which satisfy the Lipschitz shadowing property. 4. X has no singularities and X is Anosov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-15T23:01:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expansiveness",
      "c1-interior",
      "expansive divergence-free vector fields",
      "lipschitz shadowing property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.3546F"
    }
  }
}