{
  "id": "2008.12915",
  "version": "v1",
  "published": "2020-08-29T05:39:54.000Z",
  "updated": "2020-08-29T05:39:54.000Z",
  "title": "$\\mathcal{M}_n$ is connected",
  "authors": [
    "Yuto Nakajima"
  ],
  "comment": "17 pages, and 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the sets of zeros of some families of power series. We prove that the sets of zeros in the unit disk are connected. Furthermore, we apply this result to the study of the connectedness locus $\\mathcal{M}_n$ for fractal $n$-gons. We prove that for each $n$, $\\mathcal{M}_n$ is connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-29T05:39:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "power series",
      "unit disk",
      "connectedness locus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}