{
  "abstract": "Let $f$ be a pseudo-Anosov homeomorphism of a closed orientable surface of genus at least two. We prove that, for every $C^\\infty$ diffeomorphism $g$ isotopic to $f$, the exponential growth rate of the number of nonempty Nielsen classes of its iterates equals $h_{\\mathrm{top}}(g)$ if and only if $h_{\\mathrm{top}}(g)=h_{\\mathrm{top}}(f)$. Thus Nielsen growth captures the full entropy precisely for representatives minimizing entropy in their isotopy class. For $C^{1+α}$ diffeomorphisms, $α>0$, we identify this growth rate with the entropy of the global orbit quotient in Fathi's hyperbolic extension and establish Bowen's periodic-point formula for the quotient. We also prove that quotient entropy is upper semicontinuous in the $C^0$ topology throughout the isotopy class and continuous at every $C^{1+α}$ diffeomorphism, even under perturbations by arbitrary homeomorphisms in the class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26230",
  "author_total": 4,
  "authors": [
    {
      "name": "Pablo D. Carrasco"
    },
    {
      "name": "Federico Rodriguez-Hertz"
    },
    {
      "name": "Jana Rodriguez-Hertz"
    },
    {
      "name": "Raúl Ures"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6q2xmstqe31hy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26230",
  "fulltext_url": null,
  "id": "6q2xmstqe31hy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26230",
  "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": "W7223069374",
  "pdf_url": "https://arxiv.org/pdf/2610.26230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6q2xmstqe31hy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Entropy and periodic points in pseudo-Anosov isotopy classes",
  "title_text": "Entropy and periodic points in pseudo-Anosov isotopy classes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/6q2xmstqe31hy",
  "venue": "arXiv",
  "versions": []
}