Equidistribution, ergodicity and irreducibility in CAT(–1) spaces

  • Adrien Boyer

    Technion – Israel Institute of Technology, Haifa, Israel


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.

Cite this article

Adrien Boyer, Equidistribution, ergodicity and irreducibility in CAT(–1) spaces. Groups Geom. Dyn. 11 (2017), no. 3, pp. 777–818

DOI 10.4171/GGD/415