{
  "id": "1506.05181",
  "version": "v1",
  "published": "2015-06-17T01:45:36.000Z",
  "updated": "2015-06-17T01:45:36.000Z",
  "title": "On density of positive Lyapunov exponents for $C^1$ symplectic diffeomorphisms",
  "authors": [
    "Chao Liang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a 2$d-$dimensional compact connected Riemannian manifold and $\\omega$ be a symplectic form on $M$. In this paper, we prove that a symplectic diffeomorphism, with all Lyapunov exponent zero for almost everywhere, can be $C^1$ approximated by one with a positive Lyapunov exponent for a positive-measured subset of $M$. That is, the set \\[ \\left\\{ f\\in \\mathcal{S}ym^1_{\\omega}(M)\\,| \\begin{array}{ll} &\\mbox{The largest Lyapunov exponent }\\lambda_1(f,\\,x)>0\\\\ &\\mbox{ for a positive measure set } \\end{array} \\right\\} \\] is dense in $\\mathcal{S}ym^1_{\\omega}(M)$. \\end{abstract} \\end{center}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-17T01:45:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive lyapunov exponent",
      "symplectic diffeomorphism",
      "dimensional compact connected riemannian manifold",
      "lyapunov exponent zero",
      "largest lyapunov exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150605181L"
    }
  }
}