{
  "id": "1801.09806",
  "version": "v1",
  "published": "2018-01-30T00:14:47.000Z",
  "updated": "2018-01-30T00:14:47.000Z",
  "title": "A proof of Jones' conjecture",
  "authors": [
    "Jonathan Jaquette"
  ],
  "comment": "41 pages, 5 figures, 1 table",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we prove that Wright's equation $y'(t) = - \\alpha y(t-1) \\{1 + y(t)\\}$ has a unique slowly oscillating periodic solution for parameter values $\\alpha \\in (\\tfrac{\\pi}{2}, 1.9]$, up to time translation. This result proves Jones' Conjecture formulated in 1962, that there is a unique slowly oscillating periodic orbit for all $ \\alpha > \\tfrac{\\pi}{2}$. Furthermore, there are no isolas of periodic solutions to Wright's equation; all periodic orbits arise from Hopf bifurcations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-30T00:14:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "wrights equation",
      "unique slowly oscillating periodic solution",
      "periodic orbits arise",
      "unique slowly oscillating periodic orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}