{
  "id": "1803.05292",
  "version": "v1",
  "published": "2018-03-14T14:14:19.000Z",
  "updated": "2018-03-14T14:14:19.000Z",
  "title": "Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds",
  "authors": [
    "Adriano Da Silva",
    "Christoph Kawan"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For a right-invariant control system on a flag manifold $\\mathbb{F}_{\\Theta}$ of a real semisimple Lie group, we relate the $\\mathfrak{a}$-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt the concept of partial hyperbolicity from the theory of smooth dynamical systems to control-affine systems, and we completely characterize the partially hyperbolic chain control sets on $\\mathbb{F}_{\\Theta}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-14T14:14:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C10",
      "93C15",
      "37C60",
      "37D30",
      "22E46"
    ],
    "keywords": [
      "lyapunov exponents",
      "partial hyperbolicity",
      "flag manifold",
      "real semisimple lie group",
      "partially hyperbolic chain control sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}