Where can I find the proof of the following theorem:
Theorem (Reduction of Vector Fields) Let $\Omega_0\subset \mathbb R^n$ be an open set such that $0\in \Omega_0$. If $X: \Omega_0\longrightarrow \mathbb R^n$ is a $C^1$-vector field such that $X(0)\neq 0$, then there are an open set $\Omega\subset \mathbb R^n$ such that $0\in \Omega\subset \Omega_0$ and a $C^1$-diffeomorphism $\varphi: \Omega\longrightarrow \varphi(\Omega)$ such that $X|_{\Omega}$ is a constant vector field.
I heard the above theorem allows us to solve Cauchy problems.
Thanks.