  We prove that for evolution problems with normally hyperbolic trapping in
phase space, correlations decay exponentially in time. Normal hyperbolic
trapping means that the trapped set is smooth and symplectic and that the flow
is hyperbolic in directions transversal to it. Flows with this structure
include contact Anosov flows, classical flows in molecular dynamics, and null
geodesic flows for black holes metrics.
  The decay of correlations is a consequence of the existence of resonance free
strips for Green's functions (cut-off resolvents) and polynomial bounds on the
growth sof those functions in the semiclassical parameter.
