{
  "annotation_id": "45037d93-0d42-42c0-a082-e356d084e5ff",
  "date_created": "2026-03-02T18:00:35.520000Z",
  "date_modified": "2026-03-02T18:00:35.520000Z",
  "file_hash": "933ee870d64710d0a33191806582b5c1ce28dc276dd4bb6a6251ceacc221ff01",
  "private": false,
  "record": {
    "abstract": "The question: \"How many different trajectories are there on a single\ninvariant torus within the phase space of an integrable Hamiltonian system?\" is\nposed. A rigorous answer to the question is found both for the rational and the\nirrational tori. The relevant notion of non-measurable sets is discussed.",
    "arxiv_id": "physics/0103058",
    "authors": [
      "Piotr Pieranski",
      "Krzysztof W. Wojciechowski"
    ],
    "categories": [
      "physics.class-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1016/S0960-0779(01)00115-1",
    "journal_ref": "Chaos Solitons \u0026 Fractals 13, 1093 (2002)",
    "title": "On non-measurable sets and invariant tori",
    "url": "https://arxiv.org/abs/physics/0103058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "709af28c-9861-4913-ba4a-64f6e3c90690",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}