{
  "id": "math/9209221",
  "version": "v1",
  "published": "1992-09-20T00:00:00.000Z",
  "updated": "1992-09-20T00:00:00.000Z",
  "title": "Remarks on quadratic rational maps",
  "authors": [
    "John W. Milnor"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This will is an expository description of quadratic rational maps. Sections 2 through 6 are concerned with the geometry and topology of such maps. Sections 7--10 survey of some topics from the dynamics of quadratic rational maps. There are few proofs. Section 9 attempts to explore and picture moduli space by means of complex one-dimensional slices. Section 10 describes the theory of real quadratic rational maps. For convenience in exposition, some technical details have been relegated to appendices: Appendix A outlines some classical algebra. Appendix B describes the topology of the space of rational maps of degree \\[d\\]. Appendix C outlines several convenient normal forms for quadratic rational maps, and computes relations between various invariants.\\break Appendix D describes some geometry associated with the curves \\[\\Per_n(\\mu)\\subset\\M\\]. Appendix E describes totally disconnected Julia sets containing no critical points. Finally, Appendix F, written in collaboration with Tan Lei, describes an example of a connected quadratic Julia set for which no two components of the complement have a common boundary point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-09-20T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disconnected julia sets containing",
      "real quadratic rational maps",
      "convenient normal forms",
      "common boundary point",
      "connected quadratic julia set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......9221M"
    }
  }
}