{
  "id": "2505.04547",
  "version": "v1",
  "published": "2025-05-07T16:27:41.000Z",
  "updated": "2025-05-07T16:27:41.000Z",
  "title": "Birkhoff normal form via decorated trees",
  "authors": [
    "Jacob Armstrong-Goodall",
    "Yvain Bruned"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP",
    "math.DS",
    "math.RA"
  ],
  "abstract": "We derive an explicit tree based ansatz for the Birkhoff normal form up to any order in the context of Hamiltonian PDEs. To do so we make use of a tree based representation of iterated Poisson brackets to encode the nested Taylor expansions along flows of a sequence of symplectic transformations. As an example we consider the cubic Schr\\\"odinger equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-07T16:27:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff normal form",
      "decorated trees",
      "explicit tree",
      "iterated poisson brackets",
      "nested taylor expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}