{
  "id": "2203.08930",
  "version": "v1",
  "published": "2022-03-16T20:37:42.000Z",
  "updated": "2022-03-16T20:37:42.000Z",
  "title": "Some sufficient conditions for transitivity of Anosov diffeomorphisms",
  "authors": [
    "F. Micena"
  ],
  "comment": "Manuscript submited for publication. It is a more lucid and clear part of arXiv:2011.06196",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a $C^2$- Anosov diffemorphism $f: M \\rightarrow M,$ we prove that the jacobian condition $Jf^n(p) = 1,$ for every point $p$ such that $f^n(p) = p,$ implies transitivity. As application in the celebrated theory of Sinai-Ruelle-Bowen, this result allows us to state a classical theorem of Livsic-Sinai without directly assuming transitivity as a general hypothesis. A special consequence of our result is that every $C^2$-Anosov diffeomorphism, for which every point is regular, is indeed transitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-16T20:37:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov diffeomorphism",
      "sufficient conditions",
      "jacobian condition",
      "special consequence",
      "implies transitivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}