{
  "id": "1605.00044",
  "version": "v1",
  "published": "2016-04-29T23:50:40.000Z",
  "updated": "2016-04-29T23:50:40.000Z",
  "title": "Stably positive Lyapunov exponents for $SL(2,\\mathbb{R})$ linear cocycles over partially hyperbolic diffeomorphisms",
  "authors": [
    "Mauricio Poletti"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A result of Avila asserts that $SL(2,\\mathbb{R})$ cocycles with non-zero Lyapunov exponents are dense in a very general setting. In this paper, we are concerned with \\emph{stably non-zero} exponents. We consider $SL(2,\\mathbb{R})$ cocycles over partially hyperbolic diffeomorphisms. Under a hypothesis on the behavior of the cocycles over a compact center leaf of the diffeomorphism, we prove that the cocycle is accumulated by open sets where the Lyapunov exponents are non-zero. Ussing this criteria we give a class of examples where the Lyapunov exponents are non-zero in an open and dense set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-29T23:50:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37H15",
      "37D30",
      "37D25"
    ],
    "keywords": [
      "partially hyperbolic diffeomorphisms",
      "stably positive lyapunov exponents",
      "linear cocycles",
      "non-zero lyapunov exponents",
      "compact center leaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160500044P"
    }
  }
}