  We analyze the time-domain dynamics of resonators supporting exceptional
points (EPs), at which both the eigenfrequencies and the eigenmodes associated
with perfect capture of an input wave coalesce. We find that a time-domain
signature of the EP is an expansion of the class of waveforms which can be
perfectly captured. We show that such resonators have improved performance for
storage or transduction of energy. They also can be used to convert between
waveforms within this class. We analytically derive these features and
demonstrate them for several examples of coupled optical resonator systems.
