{
  "id": "1111.5554",
  "version": "v1",
  "published": "2011-11-23T17:01:43.000Z",
  "updated": "2011-11-23T17:01:43.000Z",
  "title": "Explosion of smoothness for conjugacies between multimodal maps",
  "authors": [
    "Jose F. Alves",
    "Vilton Pinheiro",
    "Alberto A. Pinto"
  ],
  "comment": "22 pages",
  "doi": "10.1112/jlms/jdt055",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \\to I$ and $g:J \\to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-23T17:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05"
    ],
    "keywords": [
      "smoothness",
      "smooth multimodal maps",
      "unimodal maps",
      "periodic attractors",
      "renormalization interval"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5554A"
    }
  }
}