Let $M$ be a smooth manifold( if necessary one can assume it is closed), $V$ be a non-vanishing vector field of $TM$.

Q: Under what condition, we can say that $\overline{\exp(tV)}$, i.e. the closure of the one-parameter group is compact?

Is there paper or research to show such a thing?

Let $M$ be a smooth manifold( if necessary one can assume it is closed), $V$ be a non-vanishing vector field of $TM$.

Q: Under what condition, we can say that $\overline{\exp(tV)}$, i.e. the closure of the one-parameter group in $Diff(M)$, is compact?

Is there paper or research to show such a thing?