{
  "abstract": "For every irrational rotation number $α$ of constant type and every $q>1$, we construct a $C^2$ circle diffeomorphism $F$ arbitrarily close to the rigid rotation $R_α$ in the combined $C^2$ and $B^2_{2,q}$ topology whose normalized conjugacy is not Lipschitz. We also prove that $F''\\in B^0_{2,1}$ implies global $C^1$ conjugacy. Thus the thresholds in the Besov summability and weak Dini scales are $q=1$ and $γ=1/2$, respectively. These results complement Herman's Baire category theorem on the residual existence of $C^2$ diffeomorphisms without $C^1$ conjugacy by providing quantitative counterexamples and sufficient conditions for differentiable conjugacy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30750",
  "author_total": 2,
  "authors": [
    {
      "name": "Junhao Li"
    },
    {
      "name": "Lin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c2nj4y6bjjmtd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30750",
  "fulltext_url": null,
  "id": "c2nj4y6bjjmtd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30750",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223262456",
  "pdf_url": "https://arxiv.org/pdf/2610.30750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c2nj4y6bjjmtd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On $C^2$ circle diffeomorphisms with rotation numbers of constant type",
  "title_text": "On C^2 circle diffeomorphisms with rotation numbers of constant type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/c2nj4y6bjjmtd",
  "venue": "arXiv",
  "versions": []
}