= Zero displacement energy for a compact set in a hyperplane
{title2=$e(A)=0\quad(A\subset\{p_n=0\}\text{ compact})$}
Use the <standard symplectic form> $\sum_jdq_j\wedge dp_j$ and convention $\iota_{X_H}\omega=-dH$. The Hamiltonian $H=\delta q_n$ translates $p_n$ by $\delta$. A fixed compactly supported cutoff equal to one near the set swept for $|\delta|\leq1$ leaves that translation unchanged on the original compact set. Its supremum norm is at most $C|\delta|$, so the translation displaces the set at arbitrarily small cost. This proves zero <Hamiltonian displacement energy> for either Hofer normalization.
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