{
  "abstract": "Let $k$ be a complete, non-archimedean. We study the dynamics of families of one-variable rational functions parametrized by Berkovich spaces over $k$ and over $\\mathbb{C}$ equipped with the hybrid norm. In both settings, we show an analogue of Mané--Sad--Sullivan's theorem about the continuity of the Julia set (in the Hausdorff topology). The non-archimedean case relies on the maximum modulus principle, which we show for analytic functions over analytic spaces without boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11545",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandre Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31py9m52arj3g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11545",
  "fulltext_url": null,
  "id": "31py9m52arj3g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11545",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221087865",
  "pdf_url": "https://arxiv.org/pdf/2610.11545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31py9m52arj3g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Continuity of the Julia sets in non-archimedean and hybrid settings",
  "title_text": "Continuity of the Julia sets in non-archimedean and hybrid settings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/31py9m52arj3g",
  "venue": "arXiv",
  "versions": []
}