{
  "abstract": "The qualitative dynamics of nonautonomous differential equations is often studied through cocycles and skew-product semiflows over a driving base. We develop a chain-recurrence reduction principle for systems admitting an equivariant attracting section and uniform asymptotic tracking. The abstract theorem determines the complete chain-attainability relation in the ambient phase space: chains may start off the attracting section, but every attainable target lies on it and is selected solely by the factor semiflow. Applied to contracting controlled skew-product semiflows, this gives exact descriptions of the chain recurrent set, chain components, Conley order, compact strictly invariant sets, attractors, basins, and dual repellers. A weighted-supremum transverse gauge yields a complete Lyapunov function for the full semiflow while preserving the recurrent values of the base. The differential hypotheses are verified through subadditive fiber-derivative growth and averaged moving-metric logarithmic norms, allowing transient expansion and non-unique ergodicity. Quantitative persistence is established for finite-window maps and smooth vector-field perturbations. The results provide a unified framework for chain recurrence, Lyapunov structure, and attractor--repeller geometry in contracting nonautonomous dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33519",
  "author_total": 1,
  "authors": [
    {
      "name": "Robert Vrabel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31njxnjv8baee.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33519",
  "fulltext_url": null,
  "id": "31njxnjv8baee",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33519",
  "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": "W7223817057",
  "pdf_url": "https://arxiv.org/pdf/2610.33519",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31njxnjv8baee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33519",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33519"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Ambient Chain-Relation Reduction in Contracting Controlled Skew-Product Semiflows",
  "title_text": "Ambient Chain-Relation Reduction in Contracting Controlled Skew-Product Semiflows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/31njxnjv8baee",
  "venue": "arXiv",
  "versions": []
}