An L1 ergodic theorem with values in a non-positively curved space via a canonical barycenter map

By Andrés Navas. Ergodic Theory and Dynamical Systems, 2011

50 citations recorded by the source corpus.

Abstract We give a general version of the Birkhoff ergodic theorem for functions taking values in non-positively curved spaces. In this setting, the notion of a Birkhoff sum is replaced by that of a barycenter along the orbits. The construction of an appropriate barycenter map is the core of this note. As a byproduct of our construction, we prove a fixed point theorem for actions by isometries on a Buseman space.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fcf85b5501e7797d8c5c906cf4c52b5d09bf1517