{
  "abstract": "Given a Finsler manifold $(M,F)$ and suitable nested regions $B_1\\subset B_2\\subset B_3$, with $M\\setminus B_1$ connected and non-contractible, as in the model case of concentric balls in $\\mathbb R^n$, $n\\geq2$, we consider conformal deformations $φ_λF$ which can be chosen so as to leave $F$ unchanged outside $B_3$ and grow on $B_2\\setminus B_1$. This growth creates an energy barrier, diverging with $λ$, that low-energy curves cannot cross. The minimax families can therefore be chosen in the path space of $M\\setminus B_1$, which contains compact subsets of arbitrarily large category. Consequently, for every $m\\in\\mathbb N$ and all sufficiently large $λ$, there exist at least $m$ geodesics joining two prescribed points, all avoiding $B_1$. This extends to the Finsler setting an idea of Capozzi, Fortunato and Greco. The same scheme applies to Randers metrics $α+β$, with $α$ deformed and $β$ unchanged, as well as to fixed-energy trajectories of non-relativistic electromagnetic systems and relativistic Lorentz-force trajectories, and light rays in spacetimes endowed with a causal Killing field. In the non-relativistic case only the scalar potential is perturbed, while the magnetic field is preserved. When the Killing field is not everywhere timelike, the Fermat principle yields a possibly singular Randers--Kropina metric on a spacelike hypersurface. Under a natural admissible category condition, combining localized barriers with Randers approximation gives $m$ Randers--Kropina geodesics with pairwise distinct lengths, equivalently $m$ future-pointing light rays with pairwise distinct arrival times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03533",
  "author_total": 3,
  "authors": [
    {
      "name": "Erasmo Caponio"
    },
    {
      "name": "Anna Valeria Germinario"
    },
    {
      "name": "Antonio Masiello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23hpr66z23p1n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03533",
  "fulltext_url": null,
  "id": "23hpr66z23p1n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03533",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7220384595",
  "pdf_url": "https://arxiv.org/pdf/2610.03533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23hpr66z23p1n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03533"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Multiplicity of Finsler geodesics and electromagnetic trajectories via localized deformations",
  "title_text": "Multiplicity of Finsler geodesics and electromagnetic trajectories via localized deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/23hpr66z23p1n",
  "venue": "arXiv",
  "versions": []
}