{
  "id": "2012.11069",
  "version": "v1",
  "published": "2020-12-21T01:12:21.000Z",
  "updated": "2020-12-21T01:12:21.000Z",
  "title": "Anosov-Katok constructions for quasi-periodic $\\mathrm{SL}(2,R)$ cocycles",
  "authors": [
    "Nikolaos Karaliolios",
    "Xu Xu",
    "Qi Zhou"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that if the frequency of the quasi-periodic $\\mathrm{SL}(2,\\R)$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\\frac{1}{2}<\\kappa<1$, the Lyapunov exponent is exactly $\\kappa$-H\\\"older continuous; the extended eigenstates of the potential have optimal sub-linear growth; and the dual operator associated a subcritical potential has power-law decay eigenfunctions. The proof is based on fibered Anosov-Katok constructions for quasi-periodic $\\mathrm{SL}(2,\\R)$ cocycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-21T01:12:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-periodic",
      "power-law decay eigenfunctions",
      "optimal sub-linear growth",
      "dual operator",
      "fibered anosov-katok constructions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}