Liouville's theorem says that for the Hamiltonian evolution of a system, the flow of points on the phase space with time is like that of an incompressible fluid i.e. the phase space density is independent of time or conserved. Also, as far as I understand, we say that the phase space volume is also conserved because the number of phase space points is neither increasing nor decreasing with time.
Can we view this conservation law as a consequence of some symmetry via Noether's theorem?
