{
  "abstract": "This paper studies non-autonomous iterations of $λe^z$, where at each step the parameter $λ$ is chosen from a bounded interval. Urbański and Zdunik introduced and developed a thermodynamic formalism for random dynamics of exponential maps, extending the autonomous result established independently by Rees and Lyubich to typical parameter sequences in $[A, B]^{\\mathbb{N}}$ with $1/e<A<B<\\infty$. In this paper, we show that the same conclusion indeed holds for all parameters in $[A, B]^{\\mathbb{N}}$, Our proof is based on carefully crafted uniform versions of pullback arguments, inspired by the original methods of Rees and Lyubich. In a related direction, Urbański and Zdunik established a non-autonomous analogue of Misiurewicz's theorem for the exponential map, later refined by Lech. We further extend their work by providing a refined condition for the Julia set to be the entire complex plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14794",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaxing Huang"
    },
    {
      "name": "Xiao Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah96pte21rry9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14794",
  "fulltext_url": null,
  "id": "ah96pte21rry9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14794",
  "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"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221756653",
  "pdf_url": "https://arxiv.org/pdf/2610.14794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah96pte21rry9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the Julia sets of the non-autonomous iteration of exponential maps",
  "title_text": "On the Julia sets of the non-autonomous iteration of exponential maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ah96pte21rry9",
  "venue": "arXiv",
  "versions": []
}