{
  "id": "1908.09347",
  "version": "v1",
  "published": "2019-08-25T15:53:30.000Z",
  "updated": "2019-08-25T15:53:30.000Z",
  "title": "Hölder regularity for the spectrum of translation flows",
  "authors": [
    "Alexander I. Bufetov",
    "Boris Solomyak"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $g\\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the H\\\"older property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], building on [10], obtained H\\\"older estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Forni's idea with the symbolic approach of [10] and prove H\\\"older regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-25T15:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37Axx",
      "37Dxx"
    ],
    "keywords": [
      "hölder regularity",
      "spectral measures",
      "arbitrary genus",
      "random markov compacta",
      "generic translation flows corresponding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}