{
  "id": "1211.6682",
  "version": "v1",
  "published": "2012-11-28T17:54:25.000Z",
  "updated": "2012-11-28T17:54:25.000Z",
  "title": "Non-periodic bifurcation for surface diffeomorphisms",
  "authors": [
    "Vanderlei Horita",
    "Nivaldo Muniz",
    "Paulo Sabini"
  ],
  "comment": "31 pages, 5 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that a \"positive probability\" subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles $\\mathcal{H}$ is constituted by Kupka-Smale diffeomorphisms: all periodic points are hyperbolic and their invariant manifolds intersect transversally. Lack of hyperbolicity arises from the presence of a tangency between a stable manifold and an unstable manifold, one of which is not associated to a periodic point. All these diffeomorphisms that we construct lie on the boundary of the same connected component of $\\mathcal{H}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-28T17:54:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F15",
      "70K50",
      "37C75"
    ],
    "keywords": [
      "surface diffeomorphisms",
      "non-periodic bifurcation",
      "periodic point",
      "construct lie",
      "hyperbolicity arises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6682H"
    }
  }
}