  We establish the existence and regularity properties of a monodromy operator
for the linearization of the cubic-quintic complex Ginzburg-Landau equation
about a periodically-stationary (breather) solution. We derive a formula for
the essential spectrum of the monodromy operator in terms of that of the
associated asymptotic linear differential operator. This result is obtained
using the theory of analytic semigroups under the assumption that the
Ginzburg-Landau equation includes a spectral filtering (diffusion) term. We
discuss applications to the stability of periodically-stationary pulses in
ultrafast fiber lasers.
