{
  "id": "1701.08342",
  "version": "v1",
  "published": "2017-01-29T01:21:46.000Z",
  "updated": "2017-01-29T01:21:46.000Z",
  "title": "Higher-dimensional attractors with absolutely continuous invariant probability",
  "authors": [
    "Carlos Bocker-Neto",
    "Ricardo Bortolotti"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider a dynamical system $T:\\mathbb{T}\\times \\mathbb{R}^{d} \\rightarrow \\mathbb{T}\\times \\mathbb{R}^{d} $ given by $ T(x,y) = (E(x), C(y) + f(x))$, where $E$ is a linear expanding map of $\\mathbb{T}$, $C$ is a linear contracting map of $\\mathbb{R}^d$ and $f$ is in $C^2(\\mathbb{T},\\mathbb{R}^d)$. We prove that if $T$ is volume expanding and $u\\geq d$, then for every $E$ there exists an open set $\\mathcal{U}$ of pairs $(C,f)$ for which the corresponding dynamic $T$ admits an absolutely continuous invariant probability. A geometrical characteristic of transversality between self-intersections of images of $\\mathbb{T}\\times\\{ 0 \\}$ is present in the dynamic of the maps in $\\mathcal{U}$. In addition, we give a condition between $E$ and $C$ under which it is possible to perturb $f$ to obtain a pair $(C,\\tilde{f})$ in $\\mathcal{U}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-29T01:21:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absolutely continuous invariant probability",
      "higher-dimensional attractors",
      "open set",
      "linear expanding map",
      "linear contracting map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}