Invariant-source secular growth in Hamiltonian transport
= Invariant-source secular growth in Hamiltonian transport
{title2=$f_t=t\,h$}
If $f_0=0$ and a nonzero time-independent source is invariant along the <Hamiltonian flow>, then the <Duhamel formula for Hamiltonian transport> gives $f_t=t h$. For the nonzero-frequency oscillator, $h=e^{-H_\omega}$ is smooth and belongs to all finite <Lp spaces>, yet its resulting solution has infinite space-time norm on $(0,\infty)$.