Journal of the
Korean Mathematical Society JKMS

We study the distribution of a dense orbit of a lattice $\Lambda$ acting by the right multiplication on the space $\Gamma\ba G$ where $G$ is a connected simple Lie group and $\G$ its lattice. We show that for $G=\SL_n(\br)$, every dense orbit is equidistributed with respect to the Euclidean norm.

Keywords: unipotent, lattice, homogeneous, equi-distribution

MSC numbers: 37A15, 22E40, 37A17