{
  "abstract": "This paper proves the integrability of a nonholonomic billiard defined by a knife-edge in a disk. The paper begins by parametrizing the impact space using coordinates that reveal the system's rotational symmetry. It then constructs a map on the space of post-impact states that encodes the billiard dynamics through a recurrence relating each post-impact state to the next. In addition, the paper shows that the knife-edge billiard admits a family of generalized caustics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12963",
  "author_total": 4,
  "authors": [
    {
      "name": "Alejandro Bravo-Doddoli"
    },
    {
      "name": "Huaidian Hou"
    },
    {
      "name": "William Clark"
    },
    {
      "name": "Anthony M. Bloch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bkw7zhdw7q5b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12963",
  "fulltext_url": null,
  "id": "7bkw7zhdw7q5b",
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  "landing_url": "https://arxiv.org/abs/2609.12963",
  "language": null,
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  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
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      "arxiv",
      "math.MP"
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7212628456",
  "pdf_url": "https://arxiv.org/pdf/2609.12963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bkw7zhdw7q5b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The Integrability of a knife-edge Billiard in a Disk",
  "title_text": "The Integrability of a knife-edge Billiard in a Disk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/7bkw7zhdw7q5b",
  "venue": "arXiv",
  "versions": []
}