{
  "abstract": "We study the structure of the centralizer of a non-elliptic holomorphic self-map of the unit disc and its relation with continuous dynamical structures. We prove that if the identity is not isolated in the centralizer of a non-elliptic self-map $φ\\in \\mathrm{Hol}(\\mathbb D)$, then $φ$ is univalent and its centralizer contains a non-trivial continuous one-parameter semigroup of holomorphic self-maps. This result provides a general criterion for the existence of continuous dynamics arising from discrete iteration. Our approach is based on the theory of holomorphic models and on simultaneous linearization techniques for commuting self-maps. In particular, we exploit recent developments on simultaneous linearization for parabolic self-maps with positive hyperbolic step. As a consequence, we obtain new sufficient conditions for the embeddability of holomorphic self-maps into continuous semigroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19225",
  "author_total": 3,
  "authors": [
    {
      "name": "Manuel D. Contreras"
    },
    {
      "name": "Santiago D\\'ıaz-Madrigal"
    },
    {
      "name": "Pavel Gumenyuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxs7e8kdahr36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19225",
  "fulltext_url": null,
  "id": "fxs7e8kdahr36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19225",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7222212003",
  "pdf_url": "https://arxiv.org/pdf/2610.19225",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxs7e8kdahr36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19225",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19225"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On generalized embeddability of a non-elliptic self-map",
  "title_text": "On generalized embeddability of a non-elliptic self-map",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fxs7e8kdahr36",
  "venue": "arXiv",
  "versions": []
}