{
  "abstract": "Let $M$ be a finite-dimensional complete Riemannian manifold of bounded geometry. We consider a time-dependent vector field $X : \\mathbb{R} \\times M \\to TM$ with $X_t:=X(t,\\cdot) \\in \\mathfrak{X}^r(M)$ for all $t \\in \\mathbb{R}$ that satisfies some further uniform continuity assumptions. We suppose that $X$ admits a globally defined integral curve $γ: \\mathbb{R} \\to M$. To any isolated subset $Ω$ of the Sacker-Sell spectrum of $t \\mapsto \\nabla X_t(γ(t))$, Sacker-Sell theory associates a subbundle $\\mathscr{N}^Ω$ of $T_γM$ invariant under $\\nabla X_t$. Under additional nonresonance conditions on $Ω$, we prove, by an application of the parameterization method (Cabré et al., 2003), the existence of an invariant topological submanifold $\\mathscr{W}^Ω\\subset \\mathbb{R} \\times M$ with $C^r$ fibers $W_t^Ω:= \\mathscr{W}^Ω\\cap \\{t\\} \\times M$ that is unique in a sufficiently smooth subclass of invariant manifolds uniformly tangent to $\\mathscr{N}^Ω$ (made precise later). We moreover show regularity of $\\mathscr{W}^Ω$ with respect to parameters, and characterize the attraction towards $\\mathscr{W}^Ω$ via a foliation in the case $Ω$ is the slowest part of the spectrum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18078",
  "author_total": 2,
  "authors": [
    {
      "name": "Gergely Buza"
    },
    {
      "name": "George Haller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adwb3e021ee2e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18078",
  "fulltext_url": null,
  "id": "adwb3e021ee2e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18078",
  "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",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221816515",
  "pdf_url": "https://arxiv.org/pdf/2610.18078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adwb3e021ee2e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "An application of the parameterization method to evolution flows associated to nonautonomous systems",
  "title_text": "An application of the parameterization method to evolution flows associated to nonautonomous systems",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:12Z",
  "url": "https://research.draconitic.com/paper/adwb3e021ee2e",
  "venue": "arXiv",
  "versions": []
}