{
  "abstract": "We study zero-speed equilibria of the Newton-Lorentz equation $\\ddot x=\\dot x\\times B(x)$ in $\\mathbf{R}^3$, which describes the motion of a charged particle in a magnetic field $B$. We prove Lyapunov instability wherever the field $B$ does not vanish (under $C^1$ regularity), and at every isolated zero of $B$ provided it is real-analytic. These results do not assume that the field is divergence-free. In contrast, we construct a compactly supported divergence-free $C^\\infty$ field that is flat at an isolated zero and makes the corresponding equilibrium Lyapunov stable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27893",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto Enciso"
    },
    {
      "name": "Daniel Peralta-Salas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14rhpathp7qxt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27893",
  "fulltext_url": null,
  "id": "14rhpathp7qxt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27893",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7223096290",
  "pdf_url": "https://arxiv.org/pdf/2610.27893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14rhpathp7qxt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Stability and instability for particle dynamics in magnetic fields",
  "title_text": "Stability and instability for particle dynamics in magnetic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/14rhpathp7qxt",
  "venue": "arXiv",
  "versions": []
}