{
  "id": "2501.02426",
  "version": "v1",
  "published": "2025-01-05T03:10:16.000Z",
  "updated": "2025-01-05T03:10:16.000Z",
  "title": "Point-wise doubling indices of measures and its application to bi-Lipschitz classification of Bedford-McMullen carpets",
  "authors": [
    "Hui Rao",
    "Yan-Li Xu",
    "Yuan Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Doubling measure was introduced by Beurling and Ahlfors in 1956 and now it becomes a basic concept in analysis on metric space. In this paper, for a measure which is not doubling, we introduce a notion of point-wise doubling index, and calculate the point-wise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we show that, except a small class of Bedford-McMullen carpets, if two Bedford-McMullen carpets are bi-Lipschitz equivalent, then they have the same fiber sequence up to a permutation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-05T03:10:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "26A16"
    ],
    "keywords": [
      "point-wise doubling index",
      "bedford-mcmullen carpets",
      "bi-lipschitz classification",
      "application",
      "uniform bernoulli measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}