{
  "abstract": "We study open billiard flows in $\\mathbb{R}^3$ generated by reflections in the exterior of at least three ellipsoids with $C^3$ boundaries. Each obstacle is congruent to $$\\tilde{K} = \\{(x,y,z)\\in \\mathbb{R}^3 : x^2+y^2+(βz)^2 \\leq r^2\\},$$ with parameter $β>1$, small radii, and centers $O_i$ lying in the plane $Γ=\\{z=0\\}$. The configuration satisfies the no-eclipse condition (H). For any Gibbs measure on the non-wandering set of the billiard ball map, we prove that if $β>1/c_1^2$, for some constant $c_1>0$ determined by the geometry of the configuration, the two positive Lyapunov exponents are distinct and positive: $λ_1(β)>λ_2(β)>0$. Moreover, $λ_2$ is independent of $β$ and corresponds to the restriction of the billiard flow to the plane $Γ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03004",
  "author_total": 2,
  "authors": [
    {
      "name": "Amal Al Dowais"
    },
    {
      "name": "Luchezar Stoyanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e4xt79f35aqm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03004",
  "fulltext_url": null,
  "id": "1e4xt79f35aqm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03004",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220385209",
  "pdf_url": "https://arxiv.org/pdf/2610.03004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e4xt79f35aqm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Some open billiards with distinct top Lyapunov exponents",
  "title_text": "Some open billiards with distinct top Lyapunov exponents",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/1e4xt79f35aqm",
  "venue": "arXiv",
  "versions": []
}