{
  "id": "2007.09220",
  "version": "v1",
  "published": "2020-07-17T20:39:24.000Z",
  "updated": "2020-07-17T20:39:24.000Z",
  "title": "The complexity threshold for the emergence of Kakutani inequivalence",
  "authors": [
    "Van Cyr",
    "Aimee Johnson",
    "Bryna Kra",
    "Ayse Sahin"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that linear complexity is the threshold for the emergence of Kakutani inequivalence for measurable systems supported on a minimal subshift. In particular, we show that there are minimal subshifts of arbitrarily low super-linear complexity that admit both loosely Bernoulli and non-loosely Bernoulli ergodic measures and that no minimal subshift with linear complexity can admit inequivalent measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-17T20:39:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "68R15"
    ],
    "keywords": [
      "kakutani inequivalence",
      "complexity threshold",
      "minimal subshift",
      "admit inequivalent measures",
      "arbitrarily low super-linear complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}