Solution
= Solution
When $\varepsilon=0$, trajectories conserve
$$
(1-\beta)x^2+(1+\beta)y^2,
$$
so 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.