{
  "id": "0812.1575",
  "version": "v1",
  "published": "2008-12-08T21:32:32.000Z",
  "updated": "2008-12-08T21:32:32.000Z",
  "title": "Reversible biholomorphic germs",
  "authors": [
    "Patrick Ahern",
    "Anthony G. O'Farrell"
  ],
  "comment": "14 pages",
  "journal": "Comput. Methods Funct. Theory 9 (2009), No. 2, 473--84",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $G$ be a group. We say that an element $f\\in G$ is {\\em reversible in} $G$ if it is conjugate to its inverse, i.e. there exists $g\\in G$ such that $g^{-1}fg=f^{-1}$. We denote the set of reversible elements by $R(G)$. For $f\\in G$, we denote by $R_f(G)$ the set (possibly empty) of {\\em reversers} of $f$, i.e. the set of $g\\in G$ such that $g^{-1}fg=f^{-1}$. We characterise the elements of $R(G)$ and describe each $R_f(G)$, where $G$ is the the group of biholomorphic germs in one complex variable. That is, we determine all solutions to the equation $ f\\circ g\\circ f = g$, in which $f$ and $g$ are holomorphic functions on some neighbourhood of the origin, with $f(0)=g(0)=0$ and $f'(0)\\not=0\\not=g'(0)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-08T21:32:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D05",
      "39B32",
      "37F99",
      "30C35"
    ],
    "keywords": [
      "reversible biholomorphic germs",
      "holomorphic functions",
      "reversible elements",
      "characterise",
      "neighbourhood"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1575A"
    }
  }
}