{
  "id": "1901.03458",
  "version": "v1",
  "published": "2019-01-11T02:25:14.000Z",
  "updated": "2019-01-11T02:25:14.000Z",
  "title": "Monotonicity of entropy for real quadratic rational maps",
  "authors": [
    "Khashayar Filom"
  ],
  "comment": "51 pages, 16 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\\mathbb{R}\\cup\\{\\infty\\}$ based on the natural partition of the corresponding moduli space $\\mathcal{M}_2(\\mathbb{R})$ into its monotonic, covering, unimodal and bimodal regions. Utilizing the theory of polynomial-like mappings, we prove that the level sets of the real entropy function $h_\\mathbb{R}$ are connected in the $(-+-)$-bimodal region and a portion of the unimodal region in $\\mathcal{M}_2(\\mathbb{R})$. Based on the numerical evidence, we conjecture that the monotonicity holds throughout the unimodal region, but we conjecture that it fails in the region of $(+-+)$-bimodal maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-11T02:25:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37E05",
      "37F10",
      "37F30",
      "37P45"
    ],
    "keywords": [
      "real quadratic rational maps",
      "unimodal region",
      "bimodal region",
      "real entropy function",
      "monotonicity holds throughout"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}