{
  "abstract": "We study real-analytic, planar, maps, at a neighbourhood of an elliptic fixed point. We construct normal forms for them, when they admit a real-analytic first integral. We prove that a second first integral, when it exists, forces their linearisation. We consider both the resonant and the non-resonant case, whether the maps preserve a symplectic form or not. The second first integral is allowed to be smooth, real-meromorphic or real-analytic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21417",
  "author_total": 1,
  "authors": [
    {
      "name": "Stavros Anastassiou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1swxt4nvk3nwx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21417",
  "fulltext_url": null,
  "id": "1swxt4nvk3nwx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21417",
  "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"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7213941944",
  "pdf_url": "https://arxiv.org/pdf/2609.21417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1swxt4nvk3nwx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Normal forms and first integrals of planar maps at elliptic fixed points",
  "title_text": "Normal forms and first integrals of planar maps at elliptic fixed points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/1swxt4nvk3nwx",
  "venue": "arXiv",
  "versions": []
}