non-linear ergodic theorems in complete non-positive curvature metric spaces

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on hadamard spaces, which include for example (possibly infinite-dimensional) complete simply connected riemannian manifolds with non-positive sectional curvature.