{
  "id": "2101.01432",
  "version": "v1",
  "published": "2021-01-05T09:53:28.000Z",
  "updated": "2021-01-05T09:53:28.000Z",
  "title": "Hamiltonian Perturbation Theory on a Lie Algebra. Application to a non-autonomous Symmetric Top",
  "authors": [
    "Lorenzo Valvo",
    "Michel Vittot"
  ],
  "comment": "Accepted for publication on DNC",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra $\\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra $\\mathbb{B}$ of $\\mathbb{V}$, when we add a perturbation the subalgebra $\\mathbb{B}$ will no longer be preserved. We show how to transform the perturbed dynamical system to preserve $\\mathbb{B}$ up to terms quadratic in the perturbation. We apply this method to study the dynamics of a non-autonomous symmetric Rigid Body. In this example our algebraic transform plays the role of Iterative Lemma in the proof of a KAM-like statement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-05T09:53:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian perturbation theory",
      "lie algebra",
      "hamiltonian system",
      "application",
      "algebraic transform plays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}