{
  "abstract": "We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation on any symplectic groupoid $\\mathcal{G} \\rightrightarrows M.$ The impact of this new algebraic approach is twofold. On the geometric side, it yields algebraic operations to approximate Lagrangian bisections of $\\mathcal{G}$ using the Butcher-Connes-Kreimer Hopf algebra and, in turn, aims at a better understanding of the group of Hamiltonian diffeomorphisms of $M.$ On the computational side, we define a new class of Poisson integrators for Hamiltonian dynamics on Poisson manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Adrien Busnot Laurent"
    },
    {
      "name": "Oscar Cosserat"
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  "bibtex": "https://research.draconitic.com/paper/e3mtevb0qz2mg.bib",
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  "id": "e3mtevb0qz2mg",
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  "landing_url": "https://hal.science/hal-05368917v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "native_subjects": [
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  "pdf_url": "https://hal.science/hal-05368917/document",
  "pmcid": null,
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  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3mtevb0qz2mg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:52Z",
      "native_id": "hal-05368917",
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      "url": "https://hal.science/hal-05368917v2"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
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    {
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      "subfield": "mathematical-physics"
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    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
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  "title": "Butcher series for Hamiltonian Poisson integrators through symplectic groupoids",
  "title_text": "Butcher series for Hamiltonian Poisson integrators through symplectic groupoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:52Z",
  "url": "https://research.draconitic.com/paper/e3mtevb0qz2mg",
  "venue": "HAL",
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}