{
  "id": "2309.09130",
  "version": "v1",
  "published": "2023-09-17T01:46:11.000Z",
  "updated": "2023-09-17T01:46:11.000Z",
  "title": "On regularity of conjugacy between linear cocycles over partially hyperbolic systems",
  "authors": [
    "Boris Kalinin",
    "Victoria Sadovskaya"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider H\\\"older continuous $GL(d,\\mathbb R)$-valued cocycles, and more generally linear cocycles, over an accessible volume-preserving center-bunched partially hyperbolic diffeomorphism. We study the regularity of a conjugacy between two cocycles. We establish continuity of a measurable conjugacy between {\\em any} constant $GL(d,\\mathbb R)$-valued cocycle and its perturbation. We deduce this from our main technical result on continuity of a measurable conjugacy between a fiber bunched linear cocycle and a cocycle with a certain block-triangular structure. The latter class covers constant cocycles with one Lyapunov exponent. We also establish a result of independent interest on continuity of measurable solutions for twisted vector-valued cohomological equations over partially hyperbolic systems. In addition, we give more general versions of earlier results on regularity of invariant subbudles, Riemannian metrics, and conformal structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-17T01:46:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37C15"
    ],
    "keywords": [
      "partially hyperbolic systems",
      "center-bunched partially hyperbolic diffeomorphism",
      "regularity",
      "volume-preserving center-bunched partially hyperbolic",
      "class covers constant cocycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}