{
  "id": "0904.2561",
  "version": "v1",
  "published": "2009-04-16T19:18:36.000Z",
  "updated": "2009-04-16T19:18:36.000Z",
  "title": "C^k-Robust transitivity for surfaces with boundary",
  "authors": [
    "Aubin Arroyo",
    "Enrique R. Pujals"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that C^1-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C^k-robustly transitive, with k greater or equal than 2. This class of diffeomorphisms are examples where a version of Palis' conjecture on surfaces with boundary, about homoclinic tangencies and uniform hyperbolicity, does not hold in the C^2-topology. This follows showing that blow-up of pseudo-Anosov diffeomorphisms on surfaces without boundary, become C^2-robustly topologically mixing diffeomorphisms on a surfaces with boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-16T19:18:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E30",
      "37G25",
      "37D50"
    ],
    "keywords": [
      "transitivity",
      "homoclinic tangencies",
      "uniform hyperbolicity",
      "pseudo-anosov diffeomorphisms",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2561A"
    }
  }
}