14 citations · 19 across the 6 of their papers we have counts for
6 papers · 1 filter
Weakly mixing group actions: a brief survey and an example
Vitaly Bergelson, Alexander Gorodnik
The first part of the paper contains a survey of weakly mixing group actions of general group, and the second part discusses a special example of a weakly mixing action -- the SL(2…
Proximality and equidistribution on the Furstenberg boundary
A. Gorodnik, F. Maucourant
Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Γa lattice in G. We prove that every Γ-orbits in…
Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary
Alexander Gorodnik, Hee Oh
Let X be a symmetric space of noncompact type and Γa lattice in the isometry group of X. We study the distribution of orbits of Γacting on the symmetric space X and its geometric b…
Uniform distribution of orbits of lattices on spaces of frames
Alexander Gorodnik
We study distribution of orbits of a lattice Γ<SL(n,R) in the the space V_{n,l} of l-frames in R^n (1\le l\le n-1). Examples of dense Γ-orbits are known from the work of Dani, Ragh…
Lattice action on the boundary of SL(n,R)
Alexander Gorodnik
Let Γbe a lattice in G=SL(n,R) and X=G/S a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establi…
Oppenheim conjecture for pairs consisting of a linear form and a quadratic form
Alexander Gorodnik
Let Q be a nondegenerate quadratic form, and L is a nonzero linear form of dimension d>3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x),L(x)):x\in Z…