{
  "id": "1001.0053",
  "version": "v4",
  "published": "2009-12-30T23:58:16.000Z",
  "updated": "2011-09-12T19:15:48.000Z",
  "title": "Rotation Vectors for Homeomorphisms of Non-Positively Curved Manifolds",
  "authors": [
    "Pablo Lessa"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown to exist for almost every orbit of such a dynamical system with respect to any invariant measure with compact support. The concept is then extended to flows and, as an application, it is shown how non-null rotation vectors can be used to construct a measurable semi-conjugacy between a given flow and the geodesic flow of a manifold.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-09-12T19:15:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E45",
      "37A99"
    ],
    "keywords": [
      "non-positively curved manifolds",
      "homeomorphisms",
      "non-null rotation vectors",
      "complete riemannian manifold",
      "compact support"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.0053L"
    }
  }
}