{
  "abstract": "We prove that every surjective topological dynamical system on a compact metric space can be approximated in the $C^0$-Gromov--Hausdorff topology by homeomorphisms with any prescribed topological entropy in $[0,+\\infty]$, even when simultaneous approximation of its sets of invariant and ergodic measures is required. We also establish a rigidity result under uniform geometric bounds in a fixed dimension: for a homeomorphism of a closed, connected Riemannian manifold, topological stability in the sense of Gromov--Hausdorff guarantees its persistence as a factor of sufficiently close perturbations within the same geometric class. This persistence prevents topological entropy from decreasing and ensures that every invariant or ergodic measure of the original system admits a lift of the same type to the perturbed system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31939",
  "author_total": 2,
  "authors": [
    {
      "name": "Richard Cubas"
    },
    {
      "name": "Jorge Crisostomo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8gfn04h7qkck3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31939",
  "fulltext_url": null,
  "id": "8gfn04h7qkck3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31939",
  "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": "W7223678045",
  "pdf_url": "https://arxiv.org/pdf/2610.31939",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8gfn04h7qkck3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31939",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31939"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Flexibility of topological entropy and factor persistence in the $C^0$-Gromov Hausdorff topology",
  "title_text": "Flexibility of topological entropy and factor persistence in the C^0-Gromov Hausdorff topology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/8gfn04h7qkck3",
  "venue": "arXiv",
  "versions": []
}