Groupes du ping-pong et géodésiques fermées en courbure -1

Abstract

We consider a class of free and discrete groups of isometries of the hyperbolic ball 𝔹 d which contain parabolic transformations and we prove that the number of closed geodesics on 𝔹 d /Γ whose length is lesser than a is equivalent to e aδ aδ, where δ is the critical exponent of the Poincaré series.