{
  "abstract": "We establish the variational characterization of the measure of maximal entropy on noncompact manifolds of nonpositive sectional curvature. Assuming that the deck transformation group contains an axial isometry with a rank-one axis and has a finite critical exponent, we prove that the supremum of the entropies of invariant probabilities equals the critical exponent and is attained if and only if the Bowen-Margulis-Sullivan (BMS) measure is finite. In that case, the measure of maximal entropy is unique and equals the normalized BMS measure. The proof combines conditional-entropy rigidity on the regular set with an HTS-based entropy exclusion on the singular set, overcoming both non-compactness and the loss of uniform hyperbolicity due to zero curvature. We also obtain mixing under a non-arithmetic length-spectrum assumption. For nonpositively curved surfaces of genus at least two, the existence of a closed Jacobi rank-one geodesic and the non-arithmeticity of the axial length spectrum are automatic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37439",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Liu"
    },
    {
      "name": "Xiaokai Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c6sm1symdw3a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37439",
  "fulltext_url": null,
  "id": "5c6sm1symdw3a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37439",
  "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.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7224082580",
  "pdf_url": "https://arxiv.org/pdf/2610.37439",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c6sm1symdw3a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37439",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37439"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Measure of Maximal Entropy for Geodesic Flows on Noncompact Manifolds of Nonpositive Curvature",
  "title_text": "Measure of Maximal Entropy for Geodesic Flows on Noncompact Manifolds of Nonpositive Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/5c6sm1symdw3a",
  "venue": "arXiv",
  "versions": []
}