= Solution
<Hamilton's equations> define phase-space <velocity> $(\dot q_i,\dot p_i)=(H_{p_i},-H_{q_i})$. Its divergence is
$$
\sum_i(\partial_{q_i}\dot q_i+\partial_{p_i}\dot p_i)=\sum_i(H_{q_ip_i}-H_{p_iq_i})=0.
$$
Thus infinitesimal <Phase-space volume>[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.
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