{
  "id": "1712.08882",
  "version": "v1",
  "published": "2017-12-24T06:45:34.000Z",
  "updated": "2017-12-24T06:45:34.000Z",
  "title": "Smooth symmetries of $\\times a$-invariant sets",
  "authors": [
    "Michael Hochman"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the smooth self-maps $f$ of $\\times a$-invariant sets $X\\subseteq[0,1]$. Under various assumptions we show that this forces $\\log f'(x)/\\log a\\in\\mathbb{Q}$ at many points in $X$. Our method combines scenery flow methods and equidistribution results in the positive entropy case, where we improve previous work of the author and Shmerkin, with a new topological variant of the scenery flow which applies in the zero-entropy case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-24T06:45:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "11K55",
      "11B30",
      "11P70"
    ],
    "keywords": [
      "invariant sets",
      "smooth symmetries",
      "scenery flow methods",
      "positive entropy case",
      "equidistribution results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}