{
  "id": "2210.16343",
  "version": "v1",
  "published": "2022-10-28T18:17:15.000Z",
  "updated": "2022-10-28T18:17:15.000Z",
  "title": "Ergodicity of explicit logarithmic cocycles over IETs",
  "authors": [
    "Przemysław Berk",
    "Frank Trujillo",
    "Corinna Ulcigrai"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit examples of ergodic $\\mathbb{R}$-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths vector, the skew-product built over the IET with the given permutation and lengths vector given by a cocycle, with symmetric, logarithmic singularities, which is \\emph{odd} when restricted to each continuity subinterval is ergodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-28T18:17:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit logarithmic cocycles",
      "ergodicity",
      "logarithmic singularities",
      "lengths vector",
      "interval exchange transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}