{
  "id": "1908.00271",
  "version": "v1",
  "published": "2019-08-01T08:49:28.000Z",
  "updated": "2019-08-01T08:49:28.000Z",
  "title": "Dimension of ergodic measures projected onto self-similar sets with overlaps",
  "authors": [
    "Thomas Jordan",
    "Ariel Rapaport"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For self-similar sets on $\\mathbb{R}$ satisfying the exponential separation condition we show that the natural projections of shift invariant ergodic measures is equal to $\\min\\{1,\\frac{h}{-\\chi}\\}$, where $h$ and $\\chi$ are the entropy and Lyapunov exponent respectively. The proof relies on Shmerkin's recent result on the $L^{q}$ dimension of self-similar measures. We also use the same method to give results on convolutions and orthogonal projections of ergodic measures projected onto self-similar sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-01T08:49:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "37C45"
    ],
    "keywords": [
      "self-similar sets",
      "shift invariant ergodic measures",
      "exponential separation condition",
      "orthogonal projections",
      "self-similar measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}