Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 331 / 3 / e / Solution

When $\epsilon =0$, trajectories conserveso they are closed ellipses around the origin. Ordinary energy measures circular radius rather than this conserved elliptical radius. Starting on the short-energy axis and rotating to the long-energy axis produces the transient amplification from part d; the state later returns, so the growth is transient despite neutral eigenvalues.