{
  "id": "2111.01309",
  "version": "v2",
  "published": "2021-11-02T00:24:51.000Z",
  "updated": "2022-07-05T21:19:38.000Z",
  "title": "Smooth local rigidity for hyperbolic toral automorphisms",
  "authors": [
    "Boris Kalinin",
    "Victoria Sadovskaya",
    "Zhenqi Jenny Wang"
  ],
  "comment": "43 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its smooth perturbation $f$ We show that if $H$ is weakly differentiable then it is $C^{1+H\\\"older}$ and, if $A$ is also weakly irreducible, then $H$ is $C^\\infty$. As a part of the proof, we establish results of independent interest on H\\\"older continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to $C^\\infty$ in prior local rigidity results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-07-05T21:19:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37C15"
    ],
    "keywords": [
      "hyperbolic toral automorphism",
      "smooth local rigidity",
      "prior local rigidity results",
      "regularity",
      "smooth perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}