Let X be a Hadamard manifold, and Γ ⊂ Is(X) a non-elementary discrete subgroup of isometries of X which contains a rank one isometry. We relate the ergodic theory of the geodesic flow of the quotient orbifold M = X/Γ to the behavior of the Poincaré series of Γ. Precisely, the aim of this paper is to extend the so-called theorem of Hopf-Tsuji-Sullivan -well-known for manifolds of pinched negative curvature -to the framework of rank one orbifolds. Moreover, we derive some important properties for

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... Γ-invariant conformal densities supported on the geometric limit set of Γ.