{
  "abstract": "In this paper we consider area-preserving twist maps $f:\\mathbf{T}^2\\to\\mathbf{T}^2$ with vertical rotation sets reduced to a single irrational number $α$. Our first result states that under these hypotheses, there exists a unique $f$-invariant foliation $\\mathcal{F}_G=\\{\\operatorname{Graph}(ϕ_t)\\}_{t\\in\\mathbf{T}^1}$, where each function $ϕ_t:\\mathbf{T}^1\\to\\mathbf{T}^1$ is $K$-Lipschitz for some constant $K=K(f)$. Moreover, we also prove that if $\\mathcal{F}_G$ is a Lipschitz foliation, then $f$ is minimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27102",
  "author_total": 2,
  "authors": [
    {
      "name": "Salvador Addas Zanata"
    },
    {
      "name": "Julian Lazaro Aguirre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch5b4g3dfdt1x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27102",
  "fulltext_url": null,
  "id": "ch5b4g3dfdt1x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27102",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214181590",
  "pdf_url": "https://arxiv.org/pdf/2609.27102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch5b4g3dfdt1x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2609.27102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Foliations and minimality for twist maps",
  "title_text": "Foliations and minimality for twist maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/ch5b4g3dfdt1x",
  "venue": "arXiv",
  "versions": []
}