  The theory of resonant generation of nonground-state Bose-Einstein
condensates is extended to Bose-condensed systems at finite temperature. The
generalization is based on the notion of representative statistical ensembles
for Bose systems with broken global gauge symmetry. Self-consistent equations
are derived describing an arbitrary nonequilibrium nonuniform Bose system. The
notion of finite-temperature topological coherent modes, coexisting with a
cloud of noncondensed atoms, is introduced. It is shown that resonant
generation of these modes is feasible for a gas of trapped Bose atoms at finite
temperature.
