{
  "id": "math/0608720",
  "version": "v1",
  "published": "2006-08-29T15:37:40.000Z",
  "updated": "2006-08-29T15:37:40.000Z",
  "title": "Topological Entropy and Partially Hyperbolic Diffeomorphisms",
  "authors": [
    "Yongxia Hua",
    "Radu Saghin",
    "Zhihong Xia"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional, then the topological entropy is locally a constant; and if the center foliation is two dimensional, then the topological entropy is continuous on the set of all $C^\\8$ diffeomorphisms. The proof uses a topological invariant we introduced; Yomdin's theorem on upper semi-continuity; Katok's theorem on lower semi-continuity for two dimensional systems and a refined Pesin-Ruelle inequality we proved for partially hyperbolic diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-29T15:37:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37A35",
      "37D30",
      "37D25"
    ],
    "keywords": [
      "partially hyperbolic diffeomorphisms",
      "topological entropy",
      "center foliation",
      "unique non-trivial homologies",
      "dimensional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8720H"
    }
  }
}