{
  "abstract": "We introduce the notion of an F-space - a set equipped with a family of generalized pseudometrics and marked points, and construct the categorical Gromov-Hausdorff distance for F-spaces. Based on this, we propose a new definition of the distance between dynamical systems, understood in a broad sense as parameterized families of maps. The main focus is on local dynamics: we prove the preservation of Lyapunov stability and asymptotic stability under limit transitions with respect to the new distance (in the latter case, assuming a common radius of attraction). It is established that the class of stable systems is a closed and nowhere dense subset in the space of compact dynamical systems. Next, we investigate the properties of the Hausdorff map, which induces an F-space structure on the family of subsets. In the final part, we introduce another modified version of the Gromov-Hausdorff distance for dynamical systems and use it to calculate the exact distance between torus translations for a non-resonant vector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02906",
  "author_total": 1,
  "authors": [
    {
      "name": "Emin Abdullaev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vt2569h5ep9v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02906",
  "fulltext_url": null,
  "id": "6vt2569h5ep9v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02906",
  "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.MG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7172521862",
  "pdf_url": "https://arxiv.org/pdf/2608.02906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vt2569h5ep9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.02906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Gromov-Hausdorff distance and stability of dynamical systems",
  "title_text": "Gromov-Hausdorff distance and stability of dynamical systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6vt2569h5ep9v",
  "venue": "arXiv",
  "versions": []
}