  The dynamics of a ring of vortices in two-dimensional Bose-Einstein
condensates (with and without an additional vortex at the center) is studied
for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped
condensate in the Thomas-Fermi limit. The sequence of ground states (within
these single-ring configurations) is determined as a function of the external
rotation frequency by comparing the free energy of the various states. For each
ground state, the Tkachenko-like excitations and the associated dynamical
stability are analyzed.
