{
  "abstract": "We study the iteration of (T(n)=ψ(n)-n), where (ψ) is the Dedekind psi function. We show that, for almost all integers, successive iterates satisfy strong asymptotic growth relations governed by (T(n)/n). As an application, we prove that for every fixed (\\ell\\ge1), the set of integers satisfying (T^{(\\ell)}(n)=n) has asymptotic density zero, and hence so does the set of periodic points of any fixed period.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06332",
  "author_total": 1,
  "authors": [
    {
      "name": "Aimin Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40q2aqyev8b0k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06332",
  "fulltext_url": null,
  "id": "40q2aqyev8b0k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06332",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212075590",
  "pdf_url": "https://arxiv.org/pdf/2609.06332",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40q2aqyev8b0k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06332",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06332"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function",
  "title_text": "Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/40q2aqyev8b0k",
  "venue": "arXiv",
  "versions": []
}