{
  "abstract": "Let $\\mathcal H$ be the space of support functions of centrally symmetric, strictly convex, compact planar bodies whose boundary is a $C^1$ curve, endowed with the $C^1$ topology. We prove that for a residual subset of $\\mathcal H$ the outer billiard maps about the associated bodies admit unbounded orbits escaping to infinity. In particular, this residual set includes support functions arbitrarily $C^1$-close to those of disks or ellipses. This provides an affirmative answer, in the strictly convex $C^1$ setting, to a famous question of Moser and Neumann concerning the existence of unbounded outer-billiard orbits. The key ingredient is a rigidity theorem: if $h\\in\\mathcal H$ has a purely singular radius-of-curvature measure, then every continuous invariant tangent graph consists entirely of periodic points. We then show that for a generic table in $\\mathcal H$ these periodic invariant graphs are absent, allowing us to construct escaping orbits via Mather's diffusing mechanism in a Birkhoff region of instability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06418",
  "author_total": 1,
  "authors": [
    {
      "name": "Alfonso Sorrentino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d503e07yhh1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06418",
  "fulltext_url": null,
  "id": "4d503e07yhh1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06418",
  "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"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220720584",
  "pdf_url": "https://arxiv.org/pdf/2610.06418",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d503e07yhh1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06418",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06418"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Unbounded orbits in $C^1$-generic centrally symmetric strictly convex outer billiards",
  "title_text": "Unbounded orbits in C^1-generic centrally symmetric strictly convex outer billiards",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4d503e07yhh1p",
  "venue": "arXiv",
  "versions": []
}