{
  "abstract": "This paper studies the topological entropy of real-analytic Liouville integrable Hamiltonian systems. We prove that the Hamiltonian flow on a compact connected regular energy hypersurface has zero topological entropy whenever a complete family of commuting real-analytic first integrals is generically independent in a connected neighborhood of that hypersurface. The proof uses finite normal expansions along minimal analytic carriers and an ergodic version of Ziglin's leading-term argument to obtain independent invariant normal polynomials, whose Poisson geometry makes all tangent Lyapunov exponents of the carriers vanish. In particular, we prove that a real-analytic Liouville integrable geodesic flow on a closed real-analytic Riemannian manifold has zero topological entropy, giving a positive answer to the conjecture proposed by Paternain in 1992.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16640",
  "author_total": 3,
  "authors": [
    {
      "name": "Fei Liu"
    },
    {
      "name": "Xiaokai Liu"
    },
    {
      "name": "Xiang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86ej7kzjkxszw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16640",
  "fulltext_url": null,
  "id": "86ej7kzjkxszw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16640",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
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      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7221807906",
  "pdf_url": "https://arxiv.org/pdf/2610.16640",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86ej7kzjkxszw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16640",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16640"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Analytic Liouville Integrable Geodesic Flow Has Zero Entropy",
  "title_text": "Analytic Liouville Integrable Geodesic Flow Has Zero Entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/86ej7kzjkxszw",
  "venue": "arXiv",
  "versions": []
}