On the critical exponent of a discrete group of hyperbolic isometries (Q1366596)

Generalizing work of Bishop-Jones in the constant curvature case, we prove that if \(M\) is a complete Riemannian manifold with pinched negative curvature and with \(\pi_1 M\) not virtually nilpotent, then the visual dimension of the set of geodesic rays, starting from a fixed based point, that are recurrent in some compact subset of \(M\), is equal to the critical exponent of \(\pi_1 M\). We also prove that the critical exponent of an infinite subgroup \(H\) of a given word hyperbolic group equals the visual dimension of the canonical limit set of \(H\).