{
  "id": "math/0306041",
  "version": "v2",
  "published": "2003-06-02T17:37:19.000Z",
  "updated": "2004-11-02T09:46:32.000Z",
  "title": "Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies",
  "authors": [
    "Yongluo Cao",
    "Stefano Luzzatto",
    "Isabel Rios"
  ],
  "comment": "10 pages, 2 figures. This is an extended version of the paper \"Hyperbolicity of periodic points for horseshoes with internal tangencies\" by S. Luzzatto and I. Rios",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the hyperbolicity of a class of horseshoes exhibiting an internal tangency, i.e. a point of homoclinic tangency accumulated by periodic points. In particular these systems are strictly not uniformly hyperbolic. However we show that all the Lyapunov exponents of all invariant measures are uniformly bounded away from 0. This is the first known example of this kind.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-02T09:46:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37G25"
    ],
    "keywords": [
      "strictly non-zero lyapunov exponents",
      "invariant measures",
      "internal tangency",
      "non-hyperbolic systems",
      "horseshoes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6041C"
    }
  }
}