{
  "abstract": "We show that any stable hypersurface of a symplectic $4$-manifold, on which the cohomology class of the symplectic form restricts to a multiple of a rational class, can be $C^\\infty$-approximated by (possibly unstable) hypersurfaces whose closed characteristics equidistribute. The cohomological condition is necessary due to a famous example of Herman. The proof combines KAM theory with recent quantitative closing lemmas for Reeb flows and area-preserving maps. As a further application, we prove that every geodesible volume-preserving vector field on a closed three-manifold can be $C^\\infty$-approximated by volume-preserving vector fields with equidistributed periodic orbits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25465",
  "author_total": 3,
  "authors": [
    {
      "name": "Robert Cardona"
    },
    {
      "name": "Oliver Edtmair"
    },
    {
      "name": "Rohil Prasad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb3mg40sqwprw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25465",
  "fulltext_url": null,
  "id": "fb3mg40sqwprw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25465",
  "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"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214077626",
  "pdf_url": "https://arxiv.org/pdf/2609.25465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fb3mg40sqwprw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "KAM splittings and equidistributed periodic orbits for stable hypersurfaces",
  "title_text": "KAM splittings and equidistributed periodic orbits for stable hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/fb3mg40sqwprw",
  "venue": "arXiv",
  "versions": []
}