{
  "id": "1709.01579",
  "version": "v1",
  "published": "2017-09-05T20:18:12.000Z",
  "updated": "2017-09-05T20:18:12.000Z",
  "title": "Set-theoretical entropies of generalized shifts",
  "authors": [
    "Zahra Nili Ahmadabadi",
    "Fatemah Ayatollah Zadeh Shirazi"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the following text for arbitrary $X$ with at least two elements, nonempty set $\\Gamma$ and self-map $\\varphi:\\Gamma\\to\\Gamma$ we prove the set-theoretical entropy of generalized shift $\\sigma_\\varphi:X^\\Gamma\\to X^\\Gamma$ ($\\sigma_\\varphi((x_\\alpha)_{\\alpha\\in\\Gamma})=(x_{\\varphi(\\alpha)})_{\\alpha\\in\\Gamma}$ (for $(x_\\alpha)_{\\alpha\\in\\Gamma}\\in X^\\Gamma$)) is either zero or infinity, moreover it is zero if and only if $\\varphi$ is quasi-periodic. We continue our study on contravariant set-theoretical entropy of generalized shift and motivate the text using counterexamples dealing with algebraic, topological, set-theoretical and contravariant set-theoretical positive entropies of generalized shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-05T20:18:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C70"
    ],
    "keywords": [
      "generalized shift",
      "contravariant set-theoretical positive entropies",
      "nonempty set",
      "contravariant set-theoretical entropy",
      "quasi-periodic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}