{
  "id": "1709.04983",
  "version": "v1",
  "published": "2017-09-14T21:29:51.000Z",
  "updated": "2017-09-14T21:29:51.000Z",
  "title": "$C^1$ density of stable ergodicity",
  "authors": [
    "A. Avila",
    "S. Crovisier",
    "A. Wilkinson"
  ],
  "comment": "58 pages, 11 figures. The long version of \"Diffeomorphisms with positive metric entropy\" arXiv:1408.4252v3 has been split in two, and this paper corresponds to the second part. The first part is available as the current version of arXiv:1408.4252",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of \"superblenders\" from hyperbolic sets with large entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-14T21:29:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable ergodicity",
      "large entropy",
      "hyperbolic sets",
      "perturbation tools",
      "linearization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}