Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S7 / 3 / a / Solution

Hamilton's equations define phase-space velocity $({\dot{q}}_i,{\dot{p}}_i)=(H_{p_i},-H_{q_i})$. Its divergence isThus infinitesimal phase-space volumes are preserved, assuming sufficient differentiability. This is Liouville's theorem; spatial density alone need not be incompressible because the statement concerns the combined coordinate-momentum space.