of [*uniform $\taumod$-regularity*]{} where one requires the divergence to be linear in terms of $d(x,\ga_nx)$. Most of the discussion in this paper will take place within the framework of $\taumod$-regular subgroups.

Classically, the asymptotic behavior of discrete subgroups $\Ga<G$ is captured by their visual limit set $\La(\Ga)$ which is the accumulation set of their orbits $\Ga x\subset X$ in the visual boundary $\geo X$. In our context of $\taumod$-regular subgroups, the visual limit set is replaced by the [*$\taumod$-limit set*]{} $\LatGa$ contained in the partial flag manifold $\Flagt=G/P_{\taumod}$ and defined as the accumulation set of $\Ga$-orbits in the bordification $X\sqcup\Flagt$ of $X$, equipped with the topology of [*flag convergence*]{} (see section \[sec:conv\]). Here, $P_{\taumod}$ is a parabolic subgroup in the conjugacy class corresponding to $\taumod$. The notion of $\taumod$-limit set extends to arbitrary discrete subgroups.

We call a $\taumod$-regular subgroup $\Ga<G$ [*nonelementary*]{} if $|\LatGa|\geq3$, and [*antipodal*]{} if it satisfies the visibility condition that any two distinct limit simplices in $\LatGa$ are antipodal. The latter means that they can be connected by a geodesic in $X$ in the sense that the geodesic is asymptotic to interior points of the simplices. It is worth noting that the action of a $\taumod$-regular antipodal 