{
  "id": "1506.06872",
  "version": "v1",
  "published": "2015-06-23T06:14:09.000Z",
  "updated": "2015-06-23T06:14:09.000Z",
  "title": "Li-Yorke haos for endrite maps with zero topological entropy and $ω$-limit sets",
  "authors": [
    "Ghassen Askri"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $X$ be a dendrite with set of endpoints $E(X)$ closed and let $f:~X \\to X$ be a continuous map with zero topological entropy. Let $P(f)$ be the set of periodic points of $f$. We prove that if $L$ is an infinite $\\omega$-limit set of $f$ then $L\\cap P(f)\\subset E(X)^{\\prime}$, where $E(X)^{\\prime}$ is the set of all accumulations points of $E(X)$. Furthermore, if $E(X)$ is countable and $L$ is uncountable then $L\\cap P(f)=\\emptyset$. We also show that if $E(X)^{\\prime}$ is finite then any uncountable $\\omega$-limit set of $f$ has a decomposition and as a consequence if $f$ has a Li-Yorke pair $(x,y)$ with $\\omega\\_f(x)$ or $\\omega\\_f(y)$ is uncountable then $f$ is Li-Yorke chaotic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-23T06:14:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero topological entropy",
      "limit set",
      "li-yorke haos",
      "endrite maps",
      "periodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}