{
  "abstract": "For any $r>1$ and any nonnegative sequence $ω(n)=o(n)$, we construct a $C^r$ sphere diffeomorphism $f$ with $h=h_{\\mathrm{top}}(f)>0$ such that \\begin{equation*} \\lim_{n\\to\\infty}\\frac1n\\log\\#\\Fix(f^n)=h, \\qquad \\sum_{n\\geqslant1}e^{-hn+ω(n)}\\#\\Fix(f^n)<\\infty. \\end{equation*} Every ergodic invariant probability measure is hyperbolic, and, apart from finitely many fixed points, all periodic points lie in a single topologically mixing homoclinic class of entropy $h$. This shows that the logarithmic periodic-point lower bound is optimal in finite regularity. In particular, we answer the finite-regularity case of Katok's periodic-point question in the negative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01980",
  "author_total": 2,
  "authors": [
    {
      "name": "Nan Ding"
    },
    {
      "name": "Yao Tong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7h6pdsgf5xj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01980",
  "fulltext_url": null,
  "id": "d7h6pdsgf5xj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01980",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01980",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7h6pdsgf5xj4.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01980",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01980"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Finite-Regularity Counterexamples to Katok's Periodic-Point Conjecture",
  "title_text": "Finite-Regularity Counterexamples to Katok's Periodic-Point Conjecture",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/d7h6pdsgf5xj4",
  "venue": "arXiv",
  "versions": []
}