Geodesic
Equidistribution, ergodicity and irreducibility in CAT(–1) spaces
Adrien Boyer1
1Technion – Israel Institute of Technology, Haifa, Israel
Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 777-818

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DOI

We prove an equidistribution theorem à la Bader–Muchnik for operator-valued measures associated with boundary representations in the context of discrete groups of isometries of CAT(–1) spaces thanks to an equidistribution theorem of T. Roblin. This result can be viewed as a von Neumann’s mean ergodic theorem for quasi-invariant measures. In particular, this approach gives a dynamical proof of the fact that boundary representations are irreducible. Moreover, we prove some equidistribution results for conformal densities using elementary techniques from harmonic analysis.
DOI : 10.4171/ggd/415
Classification : 37-XX, 43-XX
Mots-clés : Conformal densities, boundary representations, ergodic theorems, irreducibility, equidistribution

Adrien Boyer  1

1 Technion – Israel Institute of Technology, Haifa, Israel 
Adrien Boyer. Equidistribution, ergodicity and irreducibility in CAT(–1) spaces. Groups, geometry, and dynamics, Tome 11 (2017) no. 3, pp. 777-818. doi: 10.4171/ggd/415
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     year = {2017},
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