{
  "id": "1808.10156",
  "version": "v1",
  "published": "2018-08-30T07:46:42.000Z",
  "updated": "2018-08-30T07:46:42.000Z",
  "title": "Local stable and unstable sets for positive entropy $C^1$ dynamical systems",
  "authors": [
    "Shilin Feng",
    "Rui Gao",
    "Wen Huang",
    "Zeng Lian"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For any $C^1$ diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent. The mainline of our approach to this result is under the settings of topological dynamical systems, which is also applicable to infinite dimensional $C^1$ dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-30T07:46:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical systems",
      "unstable sets",
      "positive entropy",
      "local stable",
      "smooth compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}