{
  "id": "1808.07131",
  "version": "v1",
  "published": "2018-08-21T21:14:16.000Z",
  "updated": "2018-08-21T21:14:16.000Z",
  "title": "Unstable Entropy of Partially Hyperbolic Diffeomorphisms and Generic Points of Ergodic Measures",
  "authors": [
    "Gabriel Ponce"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a partially hyperbolic diffeomorphism $f:M \\rightarrow M$ defined on a compact Riemannian manifold $M$, in this paper we define the concept of unstable topological entropy of $f$ on a set $Y \\subset M$ not necessarily compact and we extend a theorem of R. Bowen proving that, for an ergodic $f$-invariant measure $\\mu$, the unstable measure theoretical entropy of $f$ is upper bounded by the unstable topological entropy of $f$ on any set of full $\\mu$-measure. We also define a notion of unstable topological entropy of $f$ using a Hausdorff dimension like characterization and we show that the unstable topological entropy of the set of generic points of an ergodic invariant measure $\\mu$ is equal to the unstable metric entropy with respect to $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T21:14:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partially hyperbolic diffeomorphism",
      "unstable topological entropy",
      "generic points",
      "ergodic measures",
      "unstable entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}