{
  "abstract": "It is shown that a symplectic isotopy with non-degenerate end-point on a closed symplectically Calabi--Yau manifold has simple periodic points of arbitrarily large period under a simple non-vanishing condition on the Morse--Novikov homology associated with its flux. The proof combines a sharp estimate for the Conley--Zehnder index under the assumption that the mean index is an even integer with a classical asymptotic iteration argument in the non-Hamiltonian Floer-theoretic setting. We also apply this estimate to the symplectic dynamics of the standard symplectic $4$-torus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02539",
  "author_total": 3,
  "authors": [
    {
      "name": "Marcelo S. Atallah"
    },
    {
      "name": "Marta Batoréo"
    },
    {
      "name": "Brayan Ferreira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4w6k1za7k2cms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02539",
  "fulltext_url": null,
  "id": "4w6k1za7k2cms",
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  "landing_url": "https://arxiv.org/abs/2610.02539",
  "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.SG"
    ],
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7220418626",
  "pdf_url": "https://arxiv.org/pdf/2610.02539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4w6k1za7k2cms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02539"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Remarks on periodic points, flux, and the mean index in symplectic dynamics",
  "title_text": "Remarks on periodic points, flux, and the mean index in symplectic dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/4w6k1za7k2cms",
  "venue": "arXiv",
  "versions": []
}