{
  "abstract": "We study parabolic implosion in a general non-autonomous setting. Let $f(w)=w+w^2+O(w^3)$ be a holomorphic germ tangent to the identity. We consider the iteration of non-autonomous perturbations of the form \\[ w_{j+1}=f(w_j)+\\varepsilon_{j,n}^2. \\] We show that, when the $\\varepsilon_{j,n}^2$'s satisfy a Lavaurs-type condition, the element $w_n$ can be described by means of a suitable Lavaurs map $L_{u_n}$, whose phase $u_n$ is an explicit function of the perturbation parameters. In particular, whenever $u_n\\to u\\in \\mathbb C$, the non-autonomous dynamics converges locally uniformly on compact subsets of the parabolic basin to the corresponding Lavaurs map $L_u$. Our study provides a general description of additive non-autonomous parabolic implosion and yields several deterministic and random convergence results as corollaries, as well as a unified proof of several previous results. As an application, we also obtain strong discontinuity results for the Julia sets of fibered holomorphic endomorphisms of $\\mathbb P^2(\\mathbb C)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2603.27686",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthieu Astorg"
    },
    {
      "name": "Fabrizio Bianchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmwde7s8djpqb.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "fmwde7s8djpqb",
  "issns": [],
  "landing_url": "https://hal.science/hal-05733139v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05733139/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmwde7s8djpqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05733139",
      "source": "hal",
      "url": "https://hal.science/hal-05733139v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Non-autonomous parabolic implosion",
  "title_text": "Non-autonomous parabolic implosion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/fmwde7s8djpqb",
  "venue": "HAL",
  "versions": []
}