{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "00WAVB68F9"
    }
  ],
  "body": "\n## Summary\n\nThe Picard operator of an initial value problem $x' = f(t, x)$, $x(t_0) = x_0$ maps a curve $\\gamma$ to $t \\mapsto x_0 + \\int_{t_0}^{t} f(s, \\gamma(s))\\, ds$.\nIts fixed points are the solutions of the problem. See the [[definition|00WAVB68F9]].\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "kind": "concept",
    "msc": [
      "34A12"
    ],
    "name": "Picard operator",
    "sources": [
      {
        "locator": "Proof sketch",
        "url": "https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem"
      }
    ],
    "tag": "07PB7HH1T9"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/07PB7HH1T9/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/07PB7HH1T9.md",
  "msc": [
    "34A12"
  ],
  "name": "Picard operator",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/07P/07PB7HH1T9.md",
  "status": null,
  "tag": "07PB7HH1T9",
  "uri": "m2://07PB7HH1T9",
  "url": "https://math2.tamnd.com/wiki/picard-operator/",
  "writing": {
    "tag": "07PB7HH1T9",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}
