{
  "id": "1910.04705",
  "version": "v1",
  "published": "2019-10-10T17:01:59.000Z",
  "updated": "2019-10-10T17:01:59.000Z",
  "title": "On the non-monotonicity of entropy for a class of real quadratic rational maps",
  "authors": [
    "Khashayar Filom",
    "Kevin M. Pilgrim"
  ],
  "comment": "30 pages, 9 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and establishes a conjecture on the failure of monotonicity for bimodal real quadratic rational maps of shape $(+-+)$ which was posed in arXiv:1901.03458 based on experimental evidence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T17:01:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37E05",
      "37F10",
      "37F30",
      "37F45"
    ],
    "keywords": [
      "bimodal real quadratic rational maps",
      "non-monotonicity",
      "moduli space",
      "entropy function",
      "experimental evidence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}