{
  "id": "2112.01436",
  "version": "v2",
  "published": "2021-12-02T17:25:24.000Z",
  "updated": "2022-09-13T11:14:56.000Z",
  "title": "Denseness of robust exponential mixing for singular-hyperbolic attracting sets",
  "authors": [
    "Vitor Araujo"
  ],
  "comment": "27 pages. Rewrote introduction and statements. Specific applications to Axiom A and Anosov flows moved to a new article in arXiv:2209.04907. arXiv admin note: substantial text overlap with arXiv:2012.13183",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "There exists a $C^2$-open and $C^1$-dense subset of vector fields exhibiting singular-hyperbolic attracting sets (with codimension-two stable bundle), in any $d$-dimensional compact manifold ($d\\ge3$), which mix exponentiallu with respect to any physical/SRB invariant probability measure. More precisely, we show that given any connected singular-hyperbolic attracting set for a $C^2$-vector field $X$, there exists a $C^1$-close multiple of $X$ of class $C^2$, generating a topologically equivalent flow, which is robustly exponentially mixing with respect to any physical measure for all vector fields in a $C^2$ neighborhood. That is, every singular-hyperbolic attracting set mixes exponentially with respect to its physical measures modulo an arbitrarily small change in the speed of the flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-13T11:14:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D25",
      "37C10",
      "37C20"
    ],
    "keywords": [
      "robust exponential mixing",
      "exhibiting singular-hyperbolic attracting sets",
      "vector field",
      "fields exhibiting singular-hyperbolic attracting",
      "attracting set mixes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}