{
  "abstract": "Let $(X,T)$ be a topological dynamical system, and let $\\dim(X,T)$ denote Meyerovitch's dynamical dimension. We prove that, for every integer $n\\geq1$, if $\\dim(X,T)<n/2$, then the set of maps $f\\in C(X,[0,1]^n)$ for which the orbit map $$ I_f: X\\longrightarrow([0,1]^n)^{\\mathbb{Z}}, \\qquad I_f(x)=\\bigl(f(T^k x)\\bigr)_{k\\in\\mathbb{Z}}, $$ is a topological embedding is a dense $G_δ$ set. Consequently, $(X,T)$ embeds into $(([0,1]^n)^{\\mathbb{Z}},σ)$ for some integer $n\\geq1$ if and only if $\\dim(X,T)<\\infty$. The constant $1/2$ and the strict inequality are optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05664",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruxi Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9m9q2r1md15sw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05664",
  "fulltext_url": null,
  "id": "9m9q2r1md15sw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05664",
  "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": "W7212030981",
  "pdf_url": "https://arxiv.org/pdf/2609.05664",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9m9q2r1md15sw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05664",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05664"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A sharp embedding theorem for topological dynamical systems",
  "title_text": "A sharp embedding theorem for topological dynamical systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/9m9q2r1md15sw",
  "venue": "arXiv",
  "versions": []
}