Let G be a connected Lie group and let Γ be a lattice in G (not necessarily co-compact). We
show that if (ut) is a unipotent one-parameter subgroup of G then every ergodic invariant …

We show that if (ut) is a one-parameter subgroup of SL (n, ℝ) consisting of unipotent
matrices, then for any ε> 0 there exists a compact subset K of SL (n, ℝ)/SL (n, ℤ) such that …

A well-known class of flows arises as follows: Let G be a semisimple Lie group and F be a
lattice in G, that is, F is a discrete subgroup such that G/F admits a finite measure invariant …

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent
sequence of probability measures on G/Γ which are invariant and ergodic under actions of …

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit
closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions …

Let G be a connected Lie group, F be a lattice in G and U={ut},~ R be a unipotent one-
parameter subgroup of G, viz. Adu is a unipotent linear transformation for all u~ U. Consider …

Let G be a Lie group and C be a closed subgroup of G. The quotient G/C is also called a
homogeneous space. To each a Є G corresponds a translation Ta given by xC→ axC. More …

Unipotent Flows and Counting Lattice Points on Homogeneous Varieties Page 1 Annals of
Mathematics, 143 (1996), 253-299 Unipotent flows and counting lattice points on homogeneous …

1. Introduction. Let G be a Lie group and F a lattice in G; that is, F is a discrete subgroup of G
such that G/F admits a finite G-invariant measure. Let u: RG be a unipotent one-parameter …

Let {gt} be a nonquasiunipotent one-parameter subgroup of a connected semisimple Lie
group G without compact factors; we prove that the set of points in a homogeneous space …