  The Ruelle resonances of a dynamical system are spectral data describing the
precise asymptotics of correlations. We classify them completely for a class of
chaotic two-dimensional maps, the linear pseudo-Anosov maps, in terms of the
action of the map on cohomology. As applications, we obtain a full description
of the distributions which are invariant under the linear flow in the stable
direction of such a linear pseudo-Anosov map, and we solve the cohomological
equation for this flow.
