{
  "id": "1901.04724",
  "version": "v1",
  "published": "2019-01-15T09:21:06.000Z",
  "updated": "2019-01-15T09:21:06.000Z",
  "title": "Spectral disjointness of rescalings of some special flows",
  "authors": [
    "Przemysław Berk",
    "Adam Kanigowski"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study self-similarity problem for two classes of flows: (1) special flows over circle rotations and under roof functions with symmetric logarithmic singularities (2) special flows over interval exchange transformations and under roof functions which are of two types * piecewise constant with one additional discontinuity which is not a discontinuity of the IET; * piecewise linear over exchanged intervals with non-zero slope. We show that if $\\{T^f_t\\}_{t\\in\\mathbb R}$ is as in (1) then for a full measure set of rotations, and for every two distinct natural numbers $K$ and $L$, we have that $\\{T^f_{Kt}\\}_{t\\in\\mathbb R}$ and $\\{T^f_{Lt}\\}_{t\\in\\mathbb R}$ are spectrally disjoint. Similarly, if $\\{T^f_t\\}_{t\\in\\mathbb R}$ is as in (2), then for a full measure set of IET's, a.e. position of the additional discontinuity (of $f$, in piecewise constant case) and every two distinct natural numbers $K$ and $L$, the flows $\\{T^f_{Kt}\\}_{t\\in\\mathbb R}$ and $\\{T^f_{Lt}\\}_{t\\in\\mathbb R}$ are spectrally disjoint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T09:21:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special flows",
      "spectral disjointness",
      "distinct natural numbers",
      "full measure set",
      "rescalings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}