{
  "abstract": "We show that exponential maps could have complicated measurable behaviours by giving two examples in the exponential family both with singular value escaping to infinity ``slowly\", one of which is recurrent (in the sense that every positive measure set will return to itself infinitely many times), while the other is non-recurrent. This also complements earlier results of Lyubich, Rees, Urbański-Zdunik, and Hemke. We also give an example of exponential maps with singular value escaping to infinity arbitrarily slow, which is a parametric analog of a result of Rempe.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03610",
  "author_total": 3,
  "authors": [
    {
      "name": "Weiwei Cui"
    },
    {
      "name": "Jiaxing Huang"
    },
    {
      "name": "Jun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0417ncbeddmrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03610",
  "fulltext_url": null,
  "id": "0417ncbeddmrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03610",
  "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": "W7208734661",
  "pdf_url": "https://arxiv.org/pdf/2609.03610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0417ncbeddmrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dynamical (non-)recurrence of escaping exponential maps",
  "title_text": "Dynamical (non-)recurrence of escaping exponential maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/0417ncbeddmrz",
  "venue": "arXiv",
  "versions": []
}