{
  "id": "2407.13741",
  "version": "v1",
  "published": "2024-07-18T17:48:45.000Z",
  "updated": "2024-07-18T17:48:45.000Z",
  "title": "Non-commuting transformations with non-converging 2-fold ergodic averages",
  "authors": [
    "Valery V. Ryzhikov"
  ],
  "comment": "in English and Russian versions",
  "categories": [
    "math.DS"
  ],
  "abstract": "In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S,T$, some set $A$ of positive finite measure and a sequence $N_m$ with $|N_{m+1}|/|N_m|\\ \\to\\infty$ such that $T^iA\\cap S^iA=\\phi$ for $i\\in [N_{4k}, N_{4k+1}]$ and $T^iA=S^iA$ for $i\\in [N_{4k+2}, N_{2k+3}]$. For the corresponding deterministic Gaussian and Poisson suspensions $S_\\circ,T_\\circ$ over $S,T$ for some $f\\in L_\\infty$ there is not a limit of $ \\frac 1 N \\sum_{n=1}^N T_\\circ^nf\\,S_\\circ^nf$ in $ L_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-18T17:48:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodic averages",
      "non-commuting transformations",
      "song shao",
      "tim austin",
      "wen huang"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}