Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature (Q1330977)

Let \(X\) be a simply connected manifold with variable negative curvature and suppose that \(\Gamma_ 0\) is a co-compact group of isometries of \(X\). The authors consider the particular case of normal subgroups \(\Gamma\) of \(\Gamma_ 0\) for which the quotient \(\Gamma_ 0/\Gamma = Z^ k\), \(k \geq 1\), and develop a method of deriving asymptotic formulae for the orbital counting function for the action of \(\Gamma\). In particular there are obtained asymptotic estimates for some groups which are not geometrically finite.