  Given a compact real hyperbolic space we study the connection between certain
phase space distributions, so called Patterson-Sullivan distributions, and
dynamical zeta functions. These zeta functions generalize logarithmic
derivatives of classical Selberg zeta functions which are defined by closed
geodesics which is data from the geodesic ow on phase space. Patterson-Sullivan
distributions are asymptotically equivalent to Wigner distributions which play
a key role in quantum ergodicity but they are also invariant under the geodesic
ow. The surface case was studied before in [AZ07] and thus the emphasis in this
work lies on the higher dimensional case.
