{
  "id": "2204.07950",
  "version": "v1",
  "published": "2022-04-17T07:40:21.000Z",
  "updated": "2022-04-17T07:40:21.000Z",
  "title": "Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts",
  "authors": [
    "Fatemah Ayatollah Zadeh Shirazi",
    "Elaheh Hakimi",
    "Arezoo Hosseini",
    "Reza Rezavand"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, for finite discrete field $F$, nonempty set $\\Gamma$, weight vector $\\mathfrak{w}=({\\mathfrak w}_\\alpha)_{\\alpha\\in\\Gamma}\\in F^\\Gamma$ and weighted generalized shift $\\sigma_{\\varphi,{\\mathfrak w}}:F^\\Gamma\\to F^\\Gamma$, we find necessary and sufficient conditions for uniform dynamical system $(F^\\Gamma,\\sigma_{\\varphi,{\\mathfrak w}})$ to be Li--Yorke chaotic. Next we find necessary and sufficient conditions for $(F^\\Gamma,\\sigma_{\\varphi,{\\mathfrak w}})$ to be Devaney chaotic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-17T07:40:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B02",
      "54H15"
    ],
    "keywords": [
      "devaney chaotic uniform dynamical systems",
      "weighted shifts",
      "sufficient conditions",
      "finite discrete field",
      "nonempty set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}