  We study stationary solutions of the damped wave equation on a compact and
smooth Riemannian manifold without boundary. In the high frequency limit, we
prove that a sequence of $\beta$-damped stationary solutions cannot be
completely concentrated in small neighborhoods of a small fixed hyperbolic
subset made of $\beta$-damped trajectories of the geodesic flow. The article
also includes an appendix (by S. Nonnenmacher and the author) where we
establish the existence of an inverse logarithmic strip without eigenvalues
below the real axis, under a pressure condition on the set of undamped
trajectories.
