  We prove that the geodesic flow on a locally CAT(-1) metric space which is
compact, or more generally convex cocompact with non-elementary fundamental
group, can be coded by a suspension flow over an irreducible shift of finite
type with H\"older roof function. This is achieved by showing that the geodesic
flow is a metric Anosov flow, and obtaining H\"older regularity of return times
for a special class of geometrically constructed local cross-sections to the
flow. We obtain a number of strong results on the dynamics of the flow with
respect to equilibrium measures for H\"older potentials. In particular, we
prove that the Bowen-Margulis measure is Bernoulli except for the exceptional
case that all closed orbit periods are integer multiples of a common constant.
We show that our techniques also extend to the geodesic flow associated to a
projective Anosov representation, which verifies that the full power of
symbolic dynamics is available in that setting.
