Let $E \subset \mathbb{R}^n$ be open, let $V:E\to \mathbb{R}^n$ be locally Lipschitz, and let $\mathcal{D}\subset \mathbb{R}\times E$ be the domain of definition of the local flow $\varphi:\mathcal{D}\to E$ for the autonomous differential equation $\dot{x}=V(x)$. Thus, for each $x\in E$, the set
is the maximal interval of definition of the solution through $x$, and the map $t\mapsto \varphi(t,x)$ is the maximal solution of $\dot{x}=V(x)$ with initial condition $\varphi(0,x)=x$.
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Then $\varphi(0,x)=x$ for every $x\in E$. Moreover, if $x\in E$, $s,t\in \mathbb{R}$, $(s,x)\in \mathcal{D}$, $(t,\varphi(s,x))\in \mathcal{D}$, and $(t+s,x)\in \mathcal{D}$, then