{
  "abstract": "Let $U$ be an arbitrary open subset of $C^1([-h,0],\\mathbb R^n)$, and let $f:U\\to\\mathbb R^n$ be continuously differentiable. Suppose that each derivative $Df(ϕ)$, $ϕ\\in U$, admits a continuous linear extension $D_ef(ϕ):C([-h,0],\\mathbb R^n)\\to\\mathbb R^n$, such that $D_ef(ϕ)χ$ depends jointly continuously on $ϕ\\in U$ and $χ\\in C([-h,0],\\mathbb R^n)$. We construct a $C^1$ diffeomorphism of $U$ onto an open subset of $C^1([-h,0],\\mathbb R^n)$ which maps the solution manifold of $x'(t)=f(x_t)$ onto an open subset of the closed subspace defined by $ϕ'(0)=0$. This resolves an open problem posed by Walther concerning regularization of the entire solution manifold. The diffeomorphism preserves the value at zero and agrees with the original history on $[-h,-τ]$ for any prescribed $τ\\in(0,h)$, and is uniformly arbitrarily close to the identity in the supremum norm. It is connected to the identity by a jointly $C^1$ family of diffeomorphisms. The same conclusions hold under the weaker assumption that the finite signed measures representing the derivatives of $f$ have no atom at zero. We also establish a corresponding theorem for separable real Hilbert-valued histories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01482",
  "author_total": 1,
  "authors": [
    {
      "name": "Lily DiPaulo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qz3sazrgdaax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01482",
  "fulltext_url": null,
  "id": "2qz3sazrgdaax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01482",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qz3sazrgdaax.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Global straightening of solution manifolds for state-dependent delay equations",
  "title_text": "Global straightening of solution manifolds for state-dependent delay equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2qz3sazrgdaax",
  "venue": "arXiv",
  "versions": []
}