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.
Ahmadi Kakavandi,B. and Amini,M. (2011). Non-linear ergodic theorems in complete non-positive curvature metric spaces. Bulletin of the Iranian Mathematical Society, 37(No. 3), 11-20.
MLA
Ahmadi Kakavandi,B. , and Amini,M. . "Non-linear ergodic theorems in complete non-positive curvature metric spaces", Bulletin of the Iranian Mathematical Society, 37, No. 3, 2011, 11-20.
HARVARD
Ahmadi Kakavandi B., Amini M. (2011). 'Non-linear ergodic theorems in complete non-positive curvature metric spaces', Bulletin of the Iranian Mathematical Society, 37(No. 3), pp. 11-20.
CHICAGO
B. Ahmadi Kakavandi and M. Amini, "Non-linear ergodic theorems in complete non-positive curvature metric spaces," Bulletin of the Iranian Mathematical Society, 37 No. 3 (2011): 11-20,
VANCOUVER
Ahmadi Kakavandi B., Amini M. Non-linear ergodic theorems in complete non-positive curvature metric spaces. BIMS, 2011; 37(No. 3): 11-20.
