{
  "annotation_id": "50a6b593-a4d6-4613-99f9-c739200aff45",
  "date_created": "2026-03-02T18:02:48.244000Z",
  "date_modified": "2026-03-02T18:02:48.244000Z",
  "file_hash": "93caf7de7c880768cbe2ec32cbb7f993e35b54adc6cc443e106513357df5bc67",
  "private": false,
  "record": {
    "abstract": "Generalizing a construction of P. Vanhaecke, we introduce a large class of\ndegenerate (i.e., associated to a degenerate Poisson bracket) completely\nintegrable systems on (a dense subset of) the space $\\R^{2d+n+1}$, called the\ngeneralized master systems. It turns out that certain generalized master\nsystems (with different Poisson brackets and different Hamiltonians) determine\nthe same Hamiltonian vector fields (and are therefore different descriptions of\nthe same Hamiltonian system), and that the Poisson brackets of these systems\nare compatible. Consequently, our class of generalized master systems actually\nconsists of a (smaller) class of completely integrable systems, and our\nconstruction yields a multi-Hamiltonian structure for these systems. As an\napplication, we construct a multi-Hamiltonian structure for the so-called\nmaster systems introduced by D. Mumford.",
    "arxiv_id": "solv-int/9402003",
    "authors": [
      "Peter Bueken"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Multi-Hamiltonian formulation for a class of degenerate completely   integrable systems",
    "url": "https://arxiv.org/abs/solv-int/9402003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "113c1bda-9e20-4210-a6a1-cc95e6cabe11",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}