If $M$ is a compact manifold and $X$ is a vector field in $M$ then $X$ generates a flow.
I know that every flow generates a vector field regardless of whether the manifold is compact or not. But I don't know how to try what I want, any suggestions? Thank you.
Edit: I know that if $M$ is a manifold and if $H$ is a local flow on $M$, then there is an induced vector field, which is defined as $X(p)=\frac{d}{dt}|_{t=0}H(t,p)$. What I want to do is prove something contrary to that, I want to prove that if $M$ is a compact manifold and if $X$ is a vector field in $M$, then there is a flow $H$ in $M$ such that $X(p)=\frac{d}{dt}|_{t=0}H(t,p)$, that is what I want.