Because flowmaps are homeomorphic maps, I was wondering if there is any literature that proves that diffeomorphism $\Phi(x)$ can be expressed as a flowmap of a certain dynamical system?

that is, for any $\varepsilon>0$ does there exist $\dot z(t)=v(z(t))$ and end time $\tau>0$ with initial value $z(0)=x$ such that $\Phi(x)=\phi_v^\tau(x)$ or $\|\Phi(x)-\phi_v^\tau(x)\|<\varepsilon$ where $\phi_v^\tau(x)=z(\tau)$?

There is another version (time-fixed) of this question in https://mathoverflow.net/questions/458459/can-orientation-preserving-diffeomorphism-in-mathbbrd-be-presented-by-flow