{
  "id": "1810.01664",
  "version": "v1",
  "published": "2018-10-03T09:57:41.000Z",
  "updated": "2018-10-03T09:57:41.000Z",
  "title": "Space of initial conditions and geometry of two 4-dimensional discrete Painlevé equations",
  "authors": [
    "Adrian Stefan Carstea",
    "Tomoyuki Takenawa"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "A geometric study of two 4-dimensional mappings is given. By the resolution of indeterminacy they are lifted to pseudo-automorphisms of rational varieties obtained from $({\\mathbb P}^1)^4$ by blowing-up along sixteen 2-dimensional subvarieties. The symmetry groups, the invariants and the degree growth rates are computed from the linearisation on the corresponding N\\'eron-Severi bilattices. It turns out that the deautonomised version of one of the mappings is a B\\\"acklund transformation of a direct product of the fourth Painlev\\'e equation which has $A_2^{(1)}+A_2^{(1)}$ type affine Weyl group symmetry, while that of the other mapping is of Noumi-Yamada's $A_5^{(1)}$ Painlev\\'e equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-03T09:57:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial conditions",
      "type affine weyl group symmetry",
      "degree growth rates",
      "fourth painleve equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}