{
  "id": "1206.2376",
  "version": "v1",
  "published": "2012-06-11T20:44:12.000Z",
  "updated": "2012-06-11T20:44:12.000Z",
  "title": "On the asymptotic expansion of maps with disconnected Julia set",
  "authors": [
    "Juan Rivera-Letelier"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the asymptotic expansion of smooth one-dimensional maps. We give an example of an interval map for which the optimal shrinking of components exponential rate is not attained for any neighborhood of a certain fixed point in the boundary of a periodic Fatou component. We prove a general result asserting that, when this happens the components do shrink exponentially, although the rate is not the optimal one. Finally, we give an example of a polynomial with real coefficients, such that all its critical points in the complex plane are real, and such that its asymptotic expansion as a complex map is strictly smaller than its asymptotic expansion as a real map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-11T20:44:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic expansion",
      "disconnected julia set",
      "components exponential rate",
      "periodic fatou component",
      "smooth one-dimensional maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2376R"
    }
  }
}