{
  "id": "2112.07094",
  "version": "v3",
  "published": "2021-12-14T01:22:11.000Z",
  "updated": "2022-02-18T00:10:47.000Z",
  "title": "Homomorphisms to $\\mathbb{R}$ of automorphism groups of zero entropy shifts",
  "authors": [
    "Omer Tamuz"
  ],
  "comment": "10 pages. Minor corrections with respect to the previous version",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We show that the automorphism group of every zero entropy infinite shift admits a \"drift\" homomorphism to $(\\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle defined on a space of asymptotic pairs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-02-18T00:10:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero entropy shifts",
      "automorphism group",
      "zero entropy infinite shift admits",
      "homomorphism arises",
      "asymptotic pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}