{
  "id": "2303.09546",
  "version": "v1",
  "published": "2023-03-16T17:56:17.000Z",
  "updated": "2023-03-16T17:56:17.000Z",
  "title": "Quasi-similarity and joining-stable invariants of ergodic actions",
  "authors": [
    "Valery V. Ryzhikov",
    "Jean-Paul Thouvenot"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of the groups with an element of infinite order. We produce joining-stable invariants considering zero $P$-entropy systems and prove an analog of Pinsker's theorem establishing the disjointness of such systems with the actions of comletely positive $P$-entropy. Then we apply Poisson suspensions to get a class of the corresponding examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T17:56:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodic actions",
      "quasi-similarity",
      "produce joining-stable invariants considering zero",
      "answering vershiks question",
      "bernoulli actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}