  In ideal MHD, the magnetic flux is advected by the plasma motion, freezing
flux-surfaces into the flow. An MHD equilibrium is reached when the flow
relaxes and force balance is achieved. We ask what classes of MHD equilibria
can be accessed from a given initial state via smooth incompressible ideal
motion. It is found that certain boundary displacements are formally not
supported. This follows from yet another investigation of the
Hahm--Kulsrud--Taylor (HKT) problem, which highlights the resonant behaviour
near a rational layer formed by a set of degenerate critical points in the
flux-function. When trying to retain the mirror symmetry of the flux-function
with respect to the resonant layer, the vector field that generates the
volume-preserving diffeomorphism vanishes at the identity to all order in the
time-like path parameter.
