Adiabatic actions do not preserve orbital closure
= Adiabatic actions do not preserve orbital closure
<Adiabatic invariance of an orbital action> preserves action values during slow regular changes, but frequencies $\partial H/\partial J_i$ can vary. Closure requires rational frequency ratios, which need not persist. A slowly added harmonic component in a <Kepler orbit> potential produces generic apsidal precession.