{
  "abstract": "Algebraic entropy measures the exponential growth of the degrees of iterates of rational self-maps. It is introduced by Bellon and Viallet in \\cite{BellonandViallet}. We study degree growth for rational maps arising from recurrences with the Laurent property, with particular emphasis on Gale--Robinson recurrences. We develop a direct method for determining the degree growth from the recurrence relation itself, reducing the problem to the study of associated max-linear, or tropical recurrences. We first obtain a closed formula for the degrees of iterates for a broad class of homogeneous quadratic Laurent recurrences. We then apply this result to the two-term Gale--Robinson family and derive an explicit quadratic growth formula with a periodic correction term. For three-term Gale--Robinson recurrences, we express the algebraic entropy in terms of the associated tropical growth rate sequence. Based on explicit computations, we formulate a conjecture for the general three-term family predicting quadratic growth with a periodic correction. We prove the conjecture for the infinite family with parameters $p=1$, $q=2$, and $r\\geq3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21627",
  "author_total": 1,
  "authors": [
    {
      "name": "Melih Emin Can"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1egggk7yzpp93.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21627",
  "fulltext_url": null,
  "id": "1egggk7yzpp93",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21627",
  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7222528396",
  "pdf_url": "https://arxiv.org/pdf/2610.21627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1egggk7yzpp93.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Degree Growth of Rational Maps with Laurent Property",
  "title_text": "Degree Growth of Rational Maps with Laurent Property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1egggk7yzpp93",
  "venue": "arXiv",
  "versions": []
}