{
  "id": "1311.5654",
  "version": "v1",
  "published": "2013-11-22T05:04:03.000Z",
  "updated": "2013-11-22T05:04:03.000Z",
  "title": "Generic Continuity of Metric Entropy for Volume-preserving Diffeomorphisms",
  "authors": [
    "Jiagang Yang",
    "Yunhua Zhou"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a compact manifold and $\\text{Diff}^1_m(M)$ be the set of $C^1$ volume-preserving diffeomorphisms of $M$. We prove that there is a residual subset $\\mathcal {R}\\subset \\text{Diff}^1_m(M)$ such that each $f\\in \\mathcal{R}$ is a continuity point of the map $g\\to h_m(g)$ from $\\text{Diff}^1_m(M)$ to $\\mathbb{R}$, where $h_m(g)$ is the metric entropy of $g$ with respect to volume measure $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-22T05:04:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric entropy",
      "volume-preserving diffeomorphisms",
      "generic continuity",
      "compact manifold",
      "residual subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.5654Y"
    }
  }
}