{
  "id": "0804.3616",
  "version": "v3",
  "published": "2008-04-22T22:38:30.000Z",
  "updated": "2013-08-16T12:30:34.000Z",
  "title": "On sensitive dependence on initial conditions and existence of physical measure for 3-flows",
  "authors": [
    "Vitor Araujo"
  ],
  "comment": "18 pages; 6 figures. To: Modelling, Optimization and BioEconomy, Eds. Alberto Pinto and David Zilberman. arXiv admin note: substantial text overlap with arXiv:math/0403273",
  "journal": "Chapter in book: Modeling, Dynamics, Optimization and Bioeconomics I, Pinto, Alberto Adrego; Zilberman, David (Eds.) Springer Proceedings in Mathematics & Statistics, Vol. 73. ISBN 978-3-319-04848-2. Springer-Verlag Berlin, 2014",
  "categories": [
    "math.DS"
  ],
  "abstract": "After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short in low dimensions, robust chaotic behavior for smooth flows ensures the existence of a physical measure.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-08-16T12:30:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D30",
      "37D45"
    ],
    "keywords": [
      "physical measure",
      "initial conditions",
      "sensitive dependence",
      "robust chaotic behavior meaning sensitiveness",
      "smooth flows ensures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.3616A"
    }
  }
}