{
  "annotation_id": "1228f929-c2a1-48a9-886e-8009b70de74e",
  "date_created": "2026-03-02T18:02:51.149000Z",
  "date_modified": "2026-03-02T18:02:51.149000Z",
  "file_hash": "aedaf2b5ed14a51ad5c1dd1354b8a957f32c017672b72336356d988ca49fc905",
  "private": false,
  "record": {
    "abstract": "We examine the validity of the results obtained with the singularity\nconfinement integrability criterion in the case of discrete Painlev\\\u0027e\nequations. The method used is based on the requirement of non-exponential\ngrowth of the homogeneous degree of the iterate of the mapping. We show that\nwhen we start from an integrable autonomous mapping and deautonomise it using\nsingularity confinement the degrees of growth of the nonautonomous mapping and\nof the autonomous one are identical. Thus this low-growth based approach is\ncompatible with the integrability of the results obtained through singularity\nconfinement. The origin of the singularity confinement property and its\nnecessary character for integrability are also analysed.",
    "arxiv_id": "solv-int/9910007",
    "authors": [
      "Y. Ohta",
      "K. M. Tamizhmani",
      "B. Grammaticos",
      "A. Ramani"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/S0375-9601(99)00670-2",
    "title": "Singularity confinement and algebraic entropy: the case of the discrete   Painlev\\\u0027e equations",
    "url": "https://arxiv.org/abs/solv-int/9910007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3ba6f769-b228-42dc-860b-16c7c006a8fc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}