{
  "abstract": "Let $f$ be a regular endomorphism of $\\mathbb{A}_{\\mathbb{C}}^N$ and let $C\\subseteq\\mathbb{A}_{\\mathbb{C}}^N$ be an irreducible curve. Suppose $C$ has an infinite intersection with the $f$-orbit of a point $x\\in\\mathbb{A}^N(\\mathbb{C})$. Then the normalization of $C$ is isomorphic to either $\\mathbb{A}^1$ or $\\mathbb{G}_m$. We prove that $C$ is $f$-periodic in the latter case, as expected by the dynamical Mordell-Lang conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29107",
  "author_total": 2,
  "authors": [
    {
      "name": "She Yang"
    },
    {
      "name": "Aoyang Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3xn8m1hgrssf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29107",
  "fulltext_url": null,
  "id": "e3xn8m1hgrssf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29107",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214301704",
  "pdf_url": "https://arxiv.org/pdf/2609.29107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3xn8m1hgrssf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the DML(1) property for regular endomorphisms of affine spaces: the $\\mathbb{G}_m$-case",
  "title_text": "On the DML(1) property for regular endomorphisms of affine spaces: the 𝔾_m-case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/e3xn8m1hgrssf",
  "venue": "arXiv",
  "versions": []
}