  In this article we investigate the dynamical properties of the geodesic flow
for a proper metric space endowed with a proper action by isometries of a group
with a contracting element. We show that the existence of a contracting
isometry is a sufficient evidence of negative curvature to carry in this
context various results borrowed from hyperbolic geometry. In particular, we
extend the so-called Hopf-Tsuji-Sullivan dichotomy proving that the geodesic
flow is either conservative and ergodic or dissipative.
