---
tag: 07PB7HH1T9
kind: concept
name: Picard operator
msc: [34A12]
sources:
  - url: https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem
    locator: Proof sketch
---

## Summary

The Picard operator of an initial value problem $x' = f(t, x)$, $x(t_0) = x_0$ maps a curve $\gamma$ to $t \mapsto x_0 + \int_{t_0}^{t} f(s, \gamma(s))\, ds$.
Its fixed points are the solutions of the problem. See the [[definition|00WAVB68F9]].