Transient growth, edge states, and repeller in rotating solid and fluid

For the classical problem of rotation a solid, we show somehow surprising behavior involving large transient growth perturbation energy that occurs when moment inertia associated to unstable axis approaches one two stable axes. In case, small but finite perturbations around this may induce total transfer axis, leading relaxation oscillations where and manifolds play role separatrix, an edge state. fluid in solid-body rotation, similar linear nonlinear dynamics apply between three inertial waves respecting triadic resonance condition. We existence be physically interpreted as case solid by quadratic invariants, helicity rotating fluid. They occur triad have helicities tend towards each other, their amplitudes are set such they same energy. happens third wave has vanishing frequency which corresponds nearly horizontal vector. An wave, perturbed small-amplitude with vector, will then periodically destroyed, its being transferred entirely although is linearly stable, resulting amplitudes. general described for particular triads valid class interactions other physical problems, conserved linked conservation so-called pseudomomentum, singles out frequency.