{
  "id": "2106.01585",
  "version": "v1",
  "published": "2021-06-03T04:13:38.000Z",
  "updated": "2021-06-03T04:13:38.000Z",
  "title": "Exponential mixing, KAM and smooth local rigidity",
  "authors": [
    "Ralf Spatzier",
    "Lei Yang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider actions of $\\Z ^r$ by ergodic automorphisms on a compact nilmanifolds for $r \\geq 2$. We show that small $C^k$ perturbations of such higher rank partially hyperbolic actions are smoothly conjugate to the original action, using a KAM scheme. The driving force for convergence of this iteration is the exponential mixing of the original action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-03T04:13:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C15",
      "37C85",
      "37J40"
    ],
    "keywords": [
      "smooth local rigidity",
      "exponential mixing",
      "original action",
      "higher rank partially hyperbolic actions",
      "compact nilmanifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}