{
  "id": "1909.11457",
  "version": "v1",
  "published": "2019-09-25T12:52:40.000Z",
  "updated": "2019-09-25T12:52:40.000Z",
  "title": "Flexibility of Lyapunov exponents with respect to two classes of measures on the torus",
  "authors": [
    "Alena Erchenko"
  ],
  "comment": "27 pages, 7 figures. Comments are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a smooth area-preserving Anosov diffeomorphism $f\\colon \\mathbb T^2\\rightarrow \\mathbb T^2$ homotopic to an Anosov automorphism $L$ of $\\mathbb T^2$. It is known that the positive Lyapunov exponent of $f$ with respect to the normalized Lebesgue measure is less than or equal to the topological entropy of $L$, which, in addition, is less than or equal to the Lyapunov exponent of $f$ with respect to the probability measure of maximal entropy. Moreover, the equalities only occur simultaneously. We show that these are the only restrictions on these two dynamical invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-25T12:52:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flexibility",
      "smooth area-preserving anosov diffeomorphism",
      "anosov automorphism",
      "positive lyapunov exponent",
      "normalized lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}