{
  "id": "0803.2916",
  "version": "v1",
  "published": "2008-03-20T01:57:12.000Z",
  "updated": "2008-03-20T01:57:12.000Z",
  "title": "Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies",
  "authors": [
    "Shin Kiriki",
    "Teruhiko Soma"
  ],
  "comment": "39 pages, 22 figures. To appear in Nonlinearity (accepted 20, March 2008)",
  "journal": "Nonlinearity 21 (2008) 1105-1140",
  "doi": "10.1088/0951-7715/21/5/011",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a dissipative saddle point. Our first theorem presents an open set in the parameter-plane such that, for any parameter value in the open set, there exists a one-parameter subfamily through this value exhibiting cubically related persistent contact-making and contact-breaking quadratic tangencies. Moreover, the second theorem shows that any such two-parameter family satisfies Wang-Young's conditions which guarantee that it exhibits a cubic polynomial-like strange attractor with an SRB measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-20T01:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C29",
      "37D45"
    ],
    "keywords": [
      "cubic homoclinic tangency",
      "persistent antimonotonic bifurcations",
      "strange attractor",
      "family satisfies wang-youngs conditions",
      "homoclinic tangency unfolding"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2008,
      "month": "May",
      "volume": 21,
      "number": 5,
      "pages": 1105
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008Nonli..21.1105K"
    }
  }
}