{
  "id": "2102.08448",
  "version": "v1",
  "published": "2021-02-16T20:57:16.000Z",
  "updated": "2021-02-16T20:57:16.000Z",
  "title": "Simplicity of Lyapunov spectrum for geodesic flows in negative curvature",
  "authors": [
    "Daniel Mitsutani"
  ],
  "comment": "32 pages, 1 figure; comments welcome",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "We study the Lyapunov spectrum of the geodesic flow of negatively curved 1/4-pinched Riemannian manifolds. We show that the space of metrics with simple Lyapunov spectrum with respect to the equilibrium state of any H\\\"older continuous potential is $C^k$ open and dense. The proof relies on a symbolic coding of the flow to apply the simplicity criterion of Avila and Viana in [AV07] and on perturbational results for $k$-jets of geodesic flows established in [KT72].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-16T20:57:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J39"
    ],
    "keywords": [
      "geodesic flow",
      "negative curvature",
      "simple lyapunov spectrum",
      "riemannian manifolds",
      "equilibrium state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}