{
  "id": "1603.07877",
  "version": "v1",
  "published": "2016-03-25T11:02:06.000Z",
  "updated": "2016-03-25T11:02:06.000Z",
  "title": "Aperiodicity at the boundary of chaos",
  "authors": [
    "Steven Hurder",
    "Ana Rechtman"
  ],
  "comment": "This paper was announced previously with the title \"Zippered laminations at the boundary of hyperbolicity\". arXiv admin note: text overlap with arXiv:1306.5025",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the dynamical properties of $C^{\\infty}$-variations of the flow on an aperiodic Kuperberg plug ${\\mathbb K}$. Our main result is that there exists a smooth 1-parameter family of plugs ${\\mathbb K}_{\\epsilon}$ for $\\epsilon \\in (-a,a)$ and $a<1$, such that: (1) The plug ${\\mathbb K}_0 = {\\mathbb K}$ is a generic Kuperberg plug; (2) For $\\epsilon <0$, the flow in the plug ${\\mathbb K}_{\\epsilon}$ has two periodic orbits that bound an invariant cylinder, all other orbits of the flow are wandering, and the flow has topological entropy zero; (3) For $\\epsilon > 0$, the flow in the plug ${\\mathbb K}_{\\epsilon}$ has positive topological entropy, and an abundance of periodic orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-25T11:02:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "37C70",
      "37B25",
      "37B40"
    ],
    "keywords": [
      "aperiodicity",
      "periodic orbits",
      "generic kuperberg plug",
      "aperiodic kuperberg plug",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}