{
  "annotation_id": "c9a5f97d-7aea-4025-a6b5-93e37d34ed5c",
  "date_created": "2026-03-02T18:00:29.418000Z",
  "date_modified": "2026-03-02T18:00:29.418000Z",
  "file_hash": "b4d44063c141d1cf2f1de92eadc0b02085dba855d9b0af820b197096656e83e7",
  "private": false,
  "record": {
    "abstract": "We give a comprehensive review of the renormalization group method for global\nand asymptotic analysis, putting an emphasis on the relevance to the classical\ntheory of envelopes and the existence of invariant manifolds of the dynamics\nunder consideration. We clarify that an essential point of the method is to\nconvert the problem from solving differential equations to obtaining suitable\ninitial (or boundary) conditions.\n  We mention that the notion of envelopes is also useful for constructing\nglobal and asymptotic behavior of wave functions of quantum systems such as the\nones with the quartic potential or double-well potential.",
    "arxiv_id": "patt-sol/9709003",
    "authors": [
      "Teiji Kunihiro"
    ],
    "categories": [
      "patt-sol",
      "hep-th",
      "nlin.PS"
    ],
    "title": "Uses of Envelopes for Global and Asymptotic Analysis; geometrical   meaning of renormalization group equation",
    "url": "https://arxiv.org/abs/patt-sol/9709003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "71dcf787-c564-4bba-86c9-9312db995a96",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}