{
  "id": "math/0202207",
  "version": "v3",
  "published": "2002-02-20T16:22:59.000Z",
  "updated": "2003-02-06T20:52:44.000Z",
  "title": "Robust transitivity and topological mixing for $C^1$-flows",
  "authors": [
    "Flavio Abdenur",
    "Artur Avila",
    "Jairo Bochi"
  ],
  "comment": "Final version, to appear in the Proceedings of the AMS",
  "journal": "Proceedings of American Mathematical Society, 132 (2004), 699-705.",
  "doi": "10.1090/S0002-9939-03-07187-9",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such that the continuation $\\Lambda_Y$ of $\\Lambda$ is a topologically mixing set for $Y$. In particular, robustly transitive flows become topologically mixing after $C^1$-perturbations. These results generalize a theorem by Bowen on the basic sets of generic Axiom A flows. We also show that the set of flows whose non-trivial homoclinic classes are topologically mixing is \\emph{not} open and dense, in general.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-02-06T20:52:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C20"
    ],
    "keywords": [
      "robust transitivity",
      "non-trivial homoclinic classes",
      "topological mixing",
      "topologically mixing",
      "generic flows"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2207A"
    }
  }
}