{
  "id": "1504.05463",
  "version": "v1",
  "published": "2015-04-21T15:20:02.000Z",
  "updated": "2015-04-21T15:20:02.000Z",
  "title": "Fixed curves near fixed points",
  "authors": [
    "Alastair Fletcher"
  ],
  "comment": "24 pages, 5 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $H$ be a composition of an $\\mathbb{R}$-linear planar mapping and $z\\mapsto z^n$. We classify the dynamics of $H$ in terms of the parameters of the $\\mathbb{R}$-linear mapping and the degree by associating a certain finite Blaschke product. We apply this classification to this situation where $z_0$ is a fixed point of a planar quasiregular mapping with constant complex dilatation in a neighbourhood of $z_0$. In particular we find how many curves there are that are fixed by $f$ and that land at $z_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-21T15:20:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed point",
      "fixed curves",
      "constant complex dilatation",
      "finite blaschke product",
      "linear planar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}