{
  "abstract": "We consider the integrable dynamics of a planar Kepler billiard in the plane bounded by a branch of a hyperbola focused at the Kepler center. As a sequel to our previous work \\cite{JZ2}, we use the existence of the foci-caustic circle to identify an elliptic curve on which the dynamics is linearized and we analyze Cayley's condition on $n$-periodic orbits in this setting. By taking various limits also we discuss the dynamics of planar Kepler billiards with boundary being a focused parabolic arc, as well as a straight line. In this last case, our approach offers a different way to deduce the elliptic curve as in \\cite{Felder}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18705",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel Jaud"
    },
    {
      "name": "Lei Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fcdaz3m7bf97w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18705",
  "fulltext_url": null,
  "id": "fcdaz3m7bf97w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18705",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213529663",
  "pdf_url": "https://arxiv.org/pdf/2609.18705",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fcdaz3m7bf97w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18705",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18705"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.class-ph",
      "subfield": "general"
    }
  ],
  "title": "Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch",
  "title_text": "Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/fcdaz3m7bf97w",
  "venue": "arXiv",
  "versions": []
}