{
  "abstract": "A generalized Hopf bifurcation takes place when varying a parameter of a (semi)dynamical system causes an attractor $K$ to become a repeller. In doing so, it expels a (parameter-dependent) family of attractors. In this paper we concentrate on two questions: (1) what do the expelled attractors look like?, and (2) can any attractor $K$ undergo a generalized Hopf bifurcation? Regarding (1), we compute the cohomology of the expelled attractors in terms of the cohomology of $K$; in the case of continuous-time dynamics this can be improved to a computation of their Borsuk shape. As for (2), we show that certain compacta cannot undergo generalized Hopf bifurcations and, when the ambient space has dimension $ \\leq 3$, give a complete topological characterization of which can.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08002",
  "author_total": 2,
  "authors": [
    {
      "name": "Héctor Barge"
    },
    {
      "name": "J. J. Sánchez-Gabites"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mzy6ks3gn1vp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08002",
  "fulltext_url": null,
  "id": "8mzy6ks3gn1vp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08002",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08002",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mzy6ks3gn1vp.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08002",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08002"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generalized Hopf bifurcations: a homological analysis and obstructions to their existence",
  "title_text": "Generalized Hopf bifurcations: a homological analysis and obstructions to their existence",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/8mzy6ks3gn1vp",
  "venue": "arXiv",
  "versions": []
}