We study the action of the fundamental group Γ of a negatively curved 3manifold M on the universal cover M of M . In particular we consider the ergodicity properties of the action and the distances by which points of M are displaced by elements of Γ. First we prove a displacement estimate for a general n-dimensional manifold with negatively pinched curvature and free fundamental group. This estimate is given in terms of the critical exponent D of the Poincaré series for Γ. For the case in which

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... n = 3, assuming that Γ is free of rank k ≥ 2, that the limit set of Γ has positive 2-dimensional Hausdorff measure, that D = 2 and that the Poincaré series diverges at the exponent 2, we prove a displacement estimate for Γ which is identical to the one given by the log(2k − 1) theorem [1] for the constant-curvature case.