  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 dissipative or conservative and ergodic.

Dynamical Systems;Group Theory;Metric Geometry