{
  "id": "1307.1182",
  "version": "v1",
  "published": "2013-07-04T01:26:09.000Z",
  "updated": "2013-07-04T01:26:09.000Z",
  "title": "Partial hyperbolicity and specification",
  "authors": [
    "Naoya Sumi",
    "Paulo Varandas",
    "Kenichiro Yamamoto"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and stable manifold of one of them coincides with the strongly stable leaf, then it does not satisfy the specification property. As an application, we prove that there exists a $C^1$-open and dense subset $\\mathcal P$ in the set of robustly non-hyperbolic transitive diffeomorphisms on a three dimensional closed manifold such that diffeomorphisms in $\\mathcal P$ do not satisfy the specification property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-04T01:26:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37C50"
    ],
    "keywords": [
      "partial hyperbolicity",
      "specification property",
      "partially hyperbolic dynamical systems",
      "robustly non-hyperbolic transitive diffeomorphisms",
      "partially hyperbolic diffeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1182S"
    }
  }
}