{
  "id": "2405.07645",
  "version": "v1",
  "published": "2024-05-13T11:06:43.000Z",
  "updated": "2024-05-13T11:06:43.000Z",
  "title": "Ergodicity of skew-products over typical IETs",
  "authors": [
    "Fernando Argentieri",
    "Przemysław Berk",
    "Frank Trujillo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \\[ \\operatorname{T_f}{[0, 1) \\times \\mathbb{R}}{[0, 1) \\times \\mathbb{R}}{(x, t)}{(T(x), t+f(x))}, \\] where $T$ is an interval exchange transformation and $f$ is a piece-wise constant function with a finite number of discontinuities. We show that such system is ergodic with respect to $\\operatorname{Leb}_{[0,1)\\times \\mathbb{R}}$ for a typical choice of parameters of $T$ and $f$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-13T11:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "37A40"
    ],
    "keywords": [
      "typical iets",
      "ergodicity",
      "skew-products",
      "infinite measure preserving systems",
      "interval exchange transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}