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

Published online by Cambridge University Press:  07 February 2012

ANDRÉS NAVAS
ANDRÉS NAVAS*
Affiliation:
Dep. de Matemáticas, Fac. de Ciencia, Univ. de Santiago, Alameda 3363, Estación Central, Santiago, Chile (email: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 2 , April 2013 , pp. 609 - 623
Copyright
©2012 Cambridge University Press

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