{
  "abstract": "The Katok examples on $S^2$ are induced by Randers metrics obtained by perturbing the round metric by the standard rotational Killing field: allowing a scaling factor of the round metric gives a two-parameter family of Randers metrics $F_{α,β}$, parametrised by positive real numbers $(α,β)$. We compute the set of all $(α,β)\\in (0,2+\\sqrt{3})^2$ for which $D^*(S^2,F^*_{α,β})$, the unit codisc bundle with respect to $F^*_{α,β}$, symplectically embeds into the round codisc bundle $D^*S^2$. This set has the structure of an infinite staircase. We also establish a dictionary between embeddings of these codisc bundles, singular $A_1$-ellipsoid embeddings, and $\\mathbb{Z} _2$-equivariant ellipsoid embeddings, showing that these embedding problems are equivalent. Furthermore, we prove the analogous results for the $\\mathbb{R} P^2$ case and discuss a broader family of examples for which this dictionary applies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35209",
  "author_total": 2,
  "authors": [
    {
      "name": "Nikolas Adaloglou"
    },
    {
      "name": "Johannes Hauber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75h8gevvmsnmb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35209",
  "fulltext_url": null,
  "id": "75h8gevvmsnmb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35209",
  "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"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214732090",
  "pdf_url": "https://arxiv.org/pdf/2609.35209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75h8gevvmsnmb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quantitative symplectic topology of Katok's examples and equivariant symplectic embeddings",
  "title_text": "Quantitative symplectic topology of Katok's examples and equivariant symplectic embeddings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/75h8gevvmsnmb",
  "venue": "arXiv",
  "versions": []
}