{
  "id": "1002.2237",
  "version": "v1",
  "published": "2010-02-11T01:02:32.000Z",
  "updated": "2010-02-11T01:02:32.000Z",
  "title": "Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps",
  "authors": [
    "D. J. W. Simpson",
    "J. D. Meiss"
  ],
  "comment": "32 pages, 10 figures",
  "journal": "Nonlinearity 23: 3091-3118 (2010)",
  "doi": "10.1088/0951-7715/23/12/006",
  "categories": [
    "math.DS"
  ],
  "abstract": "Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called \"shrinking points\". In this paper we extend our unfolding of the piecewise-linear case [{\\em Nonlinearity}, 22(5):1123-1144, 2009] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for $N$-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-11T01:02:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G10",
      "37G15",
      "37B10"
    ],
    "keywords": [
      "border-collision bifurcations",
      "continuous maps",
      "piecewise-smooth",
      "shrinking points generically occurs",
      "dimensional maps"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2010,
      "month": "Dec",
      "volume": 23,
      "number": 12,
      "pages": 3091
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010Nonli..23.3091S"
    }
  }
}