{
  "annotation_id": "e638798e-5c79-40df-bb5b-321f35a2bd48",
  "date_created": "2026-03-02T18:02:50.965000Z",
  "date_modified": "2026-03-02T18:02:50.965000Z",
  "file_hash": "8547139d81f87a2d5bad72b5002322f5919ea020ae0b24ed897820fd9c59afae",
  "private": false,
  "record": {
    "abstract": "Cubic invariants for two-dimensional Hamiltonian systems are investigated\nusing the Jacobi geometrization procedure. This approach allows for a unified\ntreatment of invariants at both fixed and arbitrary energy. In the geometric\npicture the invariant generally corresponds to a third rank Killing tensor,\nwhose existence at a fixed energy value forces the metric to satisfy a\nnonlinear integrability condition expressed in terms of a Kahler potential.\nFurther conditions, leading to a system of equations which is overdetermined\nexcept for singular cases, are added when the energy is arbitrary. As solutions\nto these equations we obtain several new superintegrable cases in addition to\nthe previously known cases. We also discover a superintegrable case where the\ncubic invariant is of a new type which can be represented by an energy\ndependent linear invariant. A complete list of all known systems which admit a\ncubic invariant at arbitrary energy is given.",
    "arxiv_id": "solv-int/9811005",
    "authors": [
      "Max Karlovini",
      "Kjell Rosquist"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1063/1.533137",
    "title": "A unified treatment of cubic invariants at fixed and arbitrary energy",
    "url": "https://arxiv.org/abs/solv-int/9811005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "605e1de4-e180-4810-98cb-fe7f08136263",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}