Uniform distribution of orbits of lattices on spaces of frames
Dynamical Systems
2007-05-23 v1
Abstract
We study distribution of orbits of a lattice \Gamma<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 \Gamma-orbits are known from the work of Dani, Raghavan, and Veech. We show that dense orbits of \Gamma are uniformly distributed in V_{n,l} with respect to an explicitly described measure. We also establish analogous result for lattices in Sp(n,R) that act on the space of isotropic n-frames.
Cite
@article{arxiv.math/0310235,
title = {Uniform distribution of orbits of lattices on spaces of frames},
author = {Alexander Gorodnik},
journal= {arXiv preprint arXiv:math/0310235},
year = {2007}
}
Comments
To be published in Duke Math. Journal, 31 pages