{
  "abstract": "Let $M$ be a finite-volume hyperbolic $d$-manifold with $d\\ge3$. We prove that the number of primitive nonsimple closed geodesics has exponential growth rate strictly smaller than $d-1$. Consequently, asymptotically almost every primitive closed geodesic in $M$ is simple. In contrast, we show that on an arithmetic hyperbolic manifold of type~I, the unit vectors tangent to nonsimple closed geodesics are dense in the unit tangent bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29855",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaolong Hans Han"
    },
    {
      "name": "Bohan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1270zs0z6vkvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29855",
  "fulltext_url": null,
  "id": "1270zs0z6vkvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29855",
  "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.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204933594",
  "pdf_url": "https://arxiv.org/pdf/2608.29855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1270zs0z6vkvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.29855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds",
  "title_text": "Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1270zs0z6vkvh",
  "venue": "arXiv",
  "versions": []
}