{
  "abstract": "Let $f,g\\in\\mathbb{C}[z]\\setminus\\mathbb{C}$ and $c\\in\\mathbb{C}[z]$. Suppose that $\\mathrm{deg}(c)=1$ if $\\mathrm{deg}(f)=\\mathrm{deg}(g)=1$. Using the theory of Presburger arithmetic, we prove that the rank-two recurrence set \\[ S_{f,g,c}^2:=\\left\\lbrace(m,n)\\in\\mathbb{Z}_{\\geq0}^2\\colon \\existsλ\\in\\mathbb{C}, f^{\\circ m}(λ)=g^{\\circ n}(λ)=c(λ)\\right\\rbrace \\] is semi-linear. This is a generalization of a theorem of Yang and Zhong for the case $m=n$. We also obtain partial results on recurrence sets for rational maps. These results are related to higher-dimensional questions of dynamical Mordell--Lang type of rank $\\leq2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.27058",
  "author_total": 1,
  "authors": [
    {
      "name": "Geng-Rui Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ycz7dn2kzz8w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.27058",
  "fulltext_url": null,
  "id": "2ycz7dn2kzz8w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.27058",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7162536079",
  "pdf_url": "https://arxiv.org/pdf/2605.27058",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ycz7dn2kzz8w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2605.27058",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.27058"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type",
  "title_text": "Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/2ycz7dn2kzz8w",
  "venue": "arXiv",
  "versions": []
}