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Furstenberg maps for CAT(0) targets of finite telescopic dimension

Published online by Cambridge University Press:  13 April 2015

URI BADER ,
BRUNO DUCHESNE  and
JEAN LÉCUREUX
URI BADER
Affiliation:
Mathematics Department, Technion - Israel Institute of Technology, Haifa, 32000, Israel email uri.bader@gmail.com
BRUNO DUCHESNE
Affiliation:
Institut Élie Cartan de Lorraine, Université de Lorraine, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France email bruno.duchesne@univ-lorraine.fr
JEAN LÉCUREUX
Affiliation:
Département de Mathématiques - Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay, France email jean.lecureux@math.u-psud.fr
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Abstract

We consider actions of locally compact groups $G$ on certain CAT(0) spaces $X$ by isometries. The CAT(0) spaces we consider have finite dimension at large scale. In case $B$ is a $G$-boundary, that is a measurable $G$-space with some amenability and ergodicity properties, we prove the existence of equivariant maps from $B$ to the visual boundary $\partial X$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 6 , September 2016 , pp. 1723 - 1742
Copyright
© Cambridge University Press, 2015 

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