Geometric Limit Sets of Higher Rank Lattices

Let G be a semisimple Lie group of R-rank at least 2 and adiscrete subgroup of G. We consider the limit set of in thegeometric boundary of the symmetric space associated with G.We define the notion of conical and horospherical limit points.In the case of irreducible non-uniform lattices, by using thetwo Tits building structures, we distinguish the location oftheir conical limit points. The limit sets of generalized Schottkygroups contained in Hilbert modular groups are studied. 2000Mathematics Subject Classification 22E40 (primary), 53C35 (secondary).