{
  "id": "1106.1707",
  "version": "v1",
  "published": "2011-06-09T05:55:08.000Z",
  "updated": "2011-06-09T05:55:08.000Z",
  "title": "Nonuniformly expanding 1d maps with logarithmic singularities",
  "authors": [
    "Hiroki Takahasi",
    "Qiudong Wang"
  ],
  "comment": "17 pages, no figure",
  "journal": "Nonlinearity 25 (2012) 533-550",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behavior. This implies the existence of \"chaotic\" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-09T05:55:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C15",
      "37D45",
      "37E10"
    ],
    "keywords": [
      "nonuniformly expanding 1d maps",
      "logarithmic singularities",
      "positive measure set",
      "derivatives blow",
      "dissipative homoclinic tangles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/25/2/533",
      "journal": "Nonlinearity",
      "year": 2012,
      "month": "Feb",
      "volume": 25,
      "number": 2,
      "pages": 533
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012Nonli..25..533T"
    }
  }
}