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

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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 amenability and ergodicity properties, we prove the existence of equivariant maps from $B$ to the visual boundary $\partial X$.
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https://hal.archives-ouvertes.fr/hal-00977894
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Submitted on : Friday, April 11, 2014 - 5:05:24 PM
Last modification on : Wednesday, November 3, 2021 - 4:49:22 AM
Long-term archiving on: : Friday, July 11, 2014 - 1:05:10 PM

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### Citation

Uri Bader, Bruno Duchesne, Jean Lécureux. Furstenberg maps for CAT(0) targets of finite telescopic dimension. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016, 36 (6), pp.1723-1742. ⟨10.1017/etds.2014.147⟩. ⟨hal-00977894⟩

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