Olivier Glorieux, Samuel Tapie

semi-simple real linear Lie group $G$. Let us fix a Cartan subspace $mathfrak

asubset mathfrak g$ of the Lie algebra of $G$. We show that if $Gamma< G$ is

a discrete group, and $Gamma’ triangleleft Gamma$ is a Zariski dense normal

subgroup, then the limit cones of $Gamma$ and $Gamma’$ in $mathfrak a$

coincide. Moreover, for all linear form $phi : mathfrak ato mathbb R$

positive on this limit cone, the critical exponents in the direction of $phi$

satisfy $displaystyle delta_phi(Gamma’) geq frac 1 2

delta_phi(Gamma)$. Eventually, we show that if $Gamma’backslash Gamma$ is

amenable, these critical exponents coincide.

2020