{
  "abstract": "We establish quantitative rigidity results for pseudo-rotations of the two-torus under a $(C,δ)$-deviation condition relative to their rotation vectors. The main ingredient is a quantitative free-disk estimate that converts bounds on orbit deviation into explicit control of the distance between the iterates and the identity map. Under such a $(C,δ)$-deviation condition, we show that Hölder continuous super-Liouvillean irrational pseudo-rotations are $C^0$-rigid with an exponential decay rate and that $C^k$ semi-irrational pseudo-rotations of strong non-Brjuno type exhibit $C^{k-1}$-rigidity with a superpolynomial decay rate. Moreover, under this deviation condition and sufficiently large irrationality measure, we show that Hölder continuous skew products on $\\mathbb{T}^2$ over circle rotations are $C^0$-rigid with a polynomial decay rate. As a consequence, all these classes satisfy Sarnak's conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26976",
  "author_total": 3,
  "authors": [
    {
      "name": "Yinshan Chang"
    },
    {
      "name": "Jian Wang"
    },
    {
      "name": "Junchang Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj4vxtvx3qayg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26976",
  "fulltext_url": null,
  "id": "bj4vxtvx3qayg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26976",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213000055",
  "pdf_url": "https://arxiv.org/pdf/2608.26976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj4vxtvx3qayg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2608.26976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Quantitative Rigidity of pseudo-rotations on the two-torus and Sarnak's conjecture",
  "title_text": "Quantitative Rigidity of pseudo-rotations on the two-torus and Sarnak's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/bj4vxtvx3qayg",
  "venue": "arXiv",
  "versions": []
}