{
  "id": "1707.09249",
  "version": "v1",
  "published": "2017-07-26T20:56:42.000Z",
  "updated": "2017-07-26T20:56:42.000Z",
  "title": "Adapted Metrics for Codimension one Singular Hyperbolic Flows",
  "authors": [
    "Luciana Salgado",
    "Vinicius Coelho"
  ],
  "comment": "17 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1204.4843",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a partially hyperbolic splitting a $C^1$ vector field $X$ on a $m$-manifold $M$, we obtain singular hyperbolicity whether $E$ is one-dimensional subspace, based on the idea of cross products. We show the existence of adapted metrics for singular hyperbolic set if it has a partially hyperbolic splitting $T_{\\Gamma}M = E \\oplus F$, where $F$ is a volume expanding subbundle, $E$ is an uniformly contracted and one-dimensional subbundle. Theses results extend previous ones from the first author and V. Ara\\'ujo.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-26T20:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D25"
    ],
    "keywords": [
      "singular hyperbolic flows",
      "adapted metrics",
      "codimension",
      "partially hyperbolic splitting",
      "singular hyperbolic set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}