{
  "id": "1503.06258",
  "version": "v1",
  "published": "2015-03-21T02:30:08.000Z",
  "updated": "2015-03-21T02:30:08.000Z",
  "title": "Takens' last problem and existence of non-trivial wandering domains",
  "authors": [
    "Shin Kiriki",
    "Teruhiko Soma"
  ],
  "comment": "55 pages, 23 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we give an answer to a version of the open problem of Floris Takens in [Nonlinearity, 21 (2008), no.3, T33-T36] which is related to historic behavior of dynamical systems. To obtain the answer, we show the existence of non-trivial wandering domains near a homoclinic tangency, which is conjectured by Colli and Vargas [Ergod. Th. & Dynam. Sys., 21 (2001), 1657-1681]. Concretely speaking, it is proved that any Newhouse open set in the $C^{r}$ topology of two-dimensional diffeomorphisms with $r \\geq 2$ is contained in the closure of the set of diffeomorphisms which have non-trivial wandering domains whose forward orbits have historic behavior. Moreover, this result implies an answer in the $C^{r}$ category to one of the open problems of van Strien [Discrete Conti. Dynam. Sys., 27 (2010), no.2, 557-588] which is concerned with wandering domains for H\\'enon family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-21T02:30:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G25",
      "37C29",
      "37D20",
      "37D25"
    ],
    "keywords": [
      "non-trivial wandering domains",
      "open problem",
      "historic behavior",
      "newhouse open set",
      "floris takens"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}