{
  "abstract": "In this paper, we study the presence of perfect powers in orbits of polynomials, or of semigroups generated by a finite family of polynomials, defined over a number field. In particular, we correct and generalize a result of Ahmadi et al. (2012), showing that multiplicative shifts of perfect powers in orbits can be detected by a finite algorithm. We also give a finiteness result on elements in orbits satisfying certain multiplicative relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00893",
  "author_total": 2,
  "authors": [
    {
      "name": "Alina Ostafe"
    },
    {
      "name": "Dat T. Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq9mtezdenn3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00893",
  "fulltext_url": null,
  "id": "eq9mtezdenn3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00893",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7216177483",
  "pdf_url": "https://arxiv.org/pdf/2610.00893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq9mtezdenn3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Powers in orbits and semigroups generated by polynomials",
  "title_text": "Powers in orbits and semigroups generated by polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/eq9mtezdenn3b",
  "venue": "arXiv",
  "versions": []
}