Liouville's theorem states that for Hamiltonian systems the phase space volume $V(t)$ is a conserved quantity, i.e., $\frac{d}{dt}V(t)=0$. This is related to the fact that trajectories in phase space do not cross and a point in phase space has a unique time evolution.
Noether's theorem tells us that conserved quantities correspond to continuous symmetries/cyclic coordinates, and vice versa.
My question is: what is the continuous symmetry/cyclic coordinate corresponding to the conservation of phase space volume?