Ergodicité et équidistribution en courbure négative

The main aim of the booklet under the review is to extend a number of results (various versions of the ergodicity theorem), which have been known already in the setting of compact Riemann surfaces with constant negative curvature to a general setting of the so called CAT(-1) spaces. The ergodicity theorem is proved for a number of cases, including the horospherical foliations, the mixing of the geodesic flow, orbital equidistribution of the group and equidistribution of primitive closed geodesics. A general unique ergodicity theorem is proved for the horosperical foliation for groups with finite Boen-Margulis-Sullivan measure. For proofs, the author uses elementary methods.

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