{
  "annotation_id": "b4535f61-c315-4aeb-ad65-0a68149f76b9",
  "date_created": "2026-03-02T18:02:51.211000Z",
  "date_modified": "2026-03-02T18:02:51.211000Z",
  "file_hash": "6afdc248236bceaa4fb8a94f0c4ac3b24f5d8affd6df1daffacaa501b96991c0",
  "private": false,
  "record": {
    "abstract": "We present a number of second order maps, which pass the singularity\nconfinement test commonly used to identify integrable discrete systems, but\nwhich nevertheless are non-integrable. As a more sensitive integrability test,\nwe propose the analysis of the complexity (``algebraic entropy\u0027\u0027) of the map\nusing the growth of the degree of its iterates: integrability is associated\nwith polynomial growth while the generic growth is exponential for chaotic\nsystems.",
    "arxiv_id": "solv-int/9711014",
    "authors": [
      "Jarmo Hietarinta",
      "Claude Viallet"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1103/PhysRevLett.81.325",
    "journal_ref": "Phys. Rev. Lett., 81 (1998) 325",
    "title": "Singularity confinement and chaos in discrete systems",
    "url": "https://arxiv.org/abs/solv-int/9711014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0faf6841-733a-4409-a205-71001ae9894f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}