The Wave Group on Asymptotically Hyperbolic Manifolds

We show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of Fourier integral operators. Then we use now standard techniques to analyze its (regularized) trace. We prove that, as in the case of compact manifolds without boundary, the singularities of the regularized wave trace are contained in the set of periods of closed geodesics. We also obtain an asymptotic expansion for the trace at zero.