{
  "id": "1205.3634",
  "version": "v3",
  "published": "2012-05-16T11:14:40.000Z",
  "updated": "2012-10-07T11:19:36.000Z",
  "title": "$R$-closed homeomorphisms on surfaces",
  "authors": [
    "Tomoo Yokoyama"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an $R$-closed homeomorphism on a connected orientable closed surface $M$. In this paper, we show that If $M$ has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If $M = \\mathbb{T}^2$ and $f$ is neither minimal nor periodic, then either each minimal set is finite disjoint union of essential circloids or there is a minimal set which is an extension of a Cantor set. If $M = \\mathbb{S}^2$ and $f$ is not periodic but orientation-preserving (resp. reversing), then the minimal sets of $f$ (resp. $f^2$) are exactly two fixed points and other circloids and $\\mathbb{S}^2/\\widetilde{f} \\cong [0, 1]$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-07T11:19:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed homeomorphism",
      "minimal set",
      "cantor set",
      "finite disjoint union",
      "essential circloids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3634Y"
    }
  }
}