{
  "id": "1907.00815",
  "version": "v1",
  "published": "2019-07-01T14:19:58.000Z",
  "updated": "2019-07-01T14:19:58.000Z",
  "title": "Random product of quasi-periodic cocycles",
  "authors": [
    "Jamerson Bezerra",
    "Mauricio Poletti"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure. We prove that the set of $C^r$, $0\\leq r \\leq \\infty$ (or analytic) $k+1$-tuples of quasi periodic cocycles taking values in $SL_2(\\mathbb{R})$ such that the random product of them has positive Lyapunov exponent contains a $C^0$ open and $C^r$ dense subset which is formed by $C^0$ continuity point of the Lyapunov exponent For $k+1$-tuples of quasi periodic cocycles taking values in $GL_d(\\mathbb{R})$ for $d>2$, we prove that if one of them is diagonal, then there exists a $C^r$ dense set of such $k+1$-tuples which has simples Lyapunov spectrum and are $C^0$ continuity point of the Lyapunov exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-01T14:19:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random product",
      "quasi-periodic cocycles",
      "quasi periodic cocycles",
      "continuity point",
      "simples lyapunov spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}