{
  "id": "1901.03013",
  "version": "v1",
  "published": "2019-01-10T04:26:53.000Z",
  "updated": "2019-01-10T04:26:53.000Z",
  "title": "The approximation of Lyapunov exponents by horseshoes for $C^1$-diffeomorphisms with dominated splitting",
  "authors": [
    "Juan Wang",
    "Rui Zou",
    "Yongluo Cao"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be a $C^1$-diffeomorphism and $\\mu$ be a hyperbolic ergodic $f$-invariant Borel probability measure with positive measure-theoretic entropy. Assume that the Oseledec splitting $$T_xM=E_1(x) \\oplus\\cdots\\oplus E_s(x) \\oplus E_{s+1}(x) \\oplus\\cdots\\oplus E_l(x) $$ is dominated on the Oseledec basin $\\Gamma$. We give extensions of Katok's Horseshoes construction. Moreover there is a dominated splitting corresponding to Oseledec subspace on horseshoes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-10T04:26:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponents",
      "dominated splitting",
      "diffeomorphism",
      "approximation",
      "invariant borel probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}