%0 Journal Article %T Non-linear ergodic theorems in complete non-positive curvature metric spaces %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Ahmadi Kakavandi, B. %A Amini, M. %D 2011 %\ 09/15/2011 %V 37 %N No. 3 %P 11-20 %! Non-linear ergodic theorems in complete non-positive curvature metric spaces %K Hadamard Space %K continuous non-expansive semigroup %K invariant mean %K asymptotic center %K non-linear ergodic theorem %R %X 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. %U http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdf