{
  "abstract": "We study multidimensional entry-exit phenomena in slow-fast systems whose fast linearization contains a nilpotent component. We show that the classical spectral balance still determines the exit point as $\\varepsilon \\to 0$, however the nilpotent component induces an algebraic amplification invisible to the spectrum, producing a $\\varepsilon|\\log\\varepsilon|$-shift of the exit point for $0 <\\varepsilon \\ll 1$. We further extend the analysis to systems with several spectral branches and show that mode dominance follows a hierarchical, lexicographic selection principle: accumulated spectral growth determines the leading order, while the nilpotent component resolves degeneracies between spectrally equivalent modes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15670",
  "author_total": 1,
  "authors": [
    {
      "name": "Jacopo Borsotti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b6x3w1fbknxx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15670",
  "fulltext_url": null,
  "id": "2b6x3w1fbknxx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15670",
  "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",
      "2612|Differential Equations and Numerical Methods"
    ]
  ],
  "openalex": "W7221771898",
  "pdf_url": "https://arxiv.org/pdf/2610.15670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b6x3w1fbknxx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The entry-exit function and nilpotent corrections in multidimensional slow-fast systems",
  "title_text": "The entry-exit function and nilpotent corrections in multidimensional slow-fast systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2b6x3w1fbknxx",
  "venue": "arXiv",
  "versions": []
}