{
  "id": "0810.3855",
  "version": "v1",
  "published": "2008-10-21T15:05:46.000Z",
  "updated": "2008-10-21T15:05:46.000Z",
  "title": "Contributions to the Geometric and Ergodic Theory of Conservative Flows",
  "authors": [
    "Mario Bessa",
    "Jorge Rocha"
  ],
  "comment": "26 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents equal to zero or its orbit has a dominated splitting. As a consequence if we have a vector field in this residual that cannot be C1-approximated by a vector field having elliptic periodic orbits, then, there exists a full measure set such that every orbit of this set admits a dominated splitting for the linear Poincare flow. Moreover, we prove that a volume-preserving and C1-stably ergodic flow can be C1-approximated by another volume-preserving flow which is non-uniformly hyperbolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-21T15:05:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D25",
      "37A99",
      "37C10"
    ],
    "keywords": [
      "ergodic theory",
      "conservative flows",
      "vector field",
      "contributions",
      "linear poincare flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3855B"
    }
  }
}