{
  "abstract": "This paper is a sequel to the authors' paper on rigidity of higher dimensional contact Anosov flows~[GRH]. At the time the authors were unaware of much earlier work of Hamenstädt~[Ham] devoted to the same problem. The methods of~[GRH] and~[Ham] are overlapping but not entirely the same. In this paper we strengthen some the results of Hamenstädt, by further bootstrapping the regularity of the conjugacy of 2-pinched contact Anosov flows. We also introduce a notion of symplecto-rigidity for symplectomorphisms and prove that some Anosov diffeomorphisms are symplecto-rigid. We further combine symplecto-rigidity with various rigidity techniques to establish a number of smooth rigidity results of Anosov symplectomorphisms. Some new phenomena are present in the realm of Anosov symplectomorphism. For example, while the well-known de la Llave example on the 4-torus demonstrates absence of rigidity in the space of smooth Anosov diffeomorphisms, however, we prove that it is rigid in the space of Anosov sympelctomorphisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10769",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrey Gogolev"
    },
    {
      "name": "Federico Rodriguez Hertz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fs3etqxw444a5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10769",
  "fulltext_url": null,
  "id": "fs3etqxw444a5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10769",
  "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": "W7212251619",
  "pdf_url": "https://arxiv.org/pdf/2609.10769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fs3etqxw444a5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10769"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Symplecto-rigidity and bootstrap for Anosov symplectomorphisms and contact Anosov flows",
  "title_text": "Symplecto-rigidity and bootstrap for Anosov symplectomorphisms and contact Anosov flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/fs3etqxw444a5",
  "venue": "arXiv",
  "versions": []
}