  We define Pollicott-Ruelle resonances for geodesic flows on noncompact
asymptotically hyperbolic negatively curved manifolds, as well as for more
general open hyperbolic systems related to Axiom A flows. These resonances are
the poles of the meromorphic continuation of the resolvent of the generator of
the flow and they describe decay of classical correlations. As an application,
we show that the Ruelle zeta function extends meromorphically to the entire
complex plane.
