{
  "id": "1408.2445",
  "version": "v2",
  "published": "2014-08-11T15:41:17.000Z",
  "updated": "2014-08-26T02:25:36.000Z",
  "title": "Ergodicity and Conservativity of products of infinite transformations and their inverses",
  "authors": [
    "Julien Clancy",
    "Rina Friedberg",
    "Indraneel Kasmalkar",
    "Isaac Loh",
    "Tudor Pădurariu",
    "Cesar E. Silva",
    "Sahana Vasudevan"
  ],
  "comment": "A new section (current section 6) on higher powers; minor renumbering of sections and minor corrections",
  "categories": [
    "math.DS"
  ],
  "abstract": "We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\\times T$ of the transformation with itself is ergodic, but the product $T\\times T^{-1}$ of the transformation with its inverse is not ergodic, and examples where all products of distinct positive powers of $T$ are ergodic but $T\\times T^{-1}$ is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-11T15:41:17.000Z",
      "abstract": "We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\\times T$ of the transformation with itself is ergodic, but the product of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-26T02:25:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A40",
      "37A05"
    ],
    "keywords": [
      "infinite transformations",
      "ergodicity",
      "conservativity",
      "infinite measure-preserving conservative ergodic markov",
      "measure-preserving conservative ergodic markov shifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2445C"
    }
  }
}