Friendly measures, homogeneous flows and singular vectors
Number Theory
2007-05-23 v1 Dynamical Systems
Abstract
We prove that singular vectors have measure zero with respect to any friendly measure on (e.g. the volume measure on a nondegenerate submanifold). This generalizes special cases considered by Davenport-Schmidt, Baker and Bugeaud. The main tool is quantitative nondivergence estimates for quasi-polynomial flows on homogeneous spaces.
Cite
@article{arxiv.math/0506513,
title = {Friendly measures, homogeneous flows and singular vectors},
author = {Dmitry Kleinbock and Barak Weiss},
journal= {arXiv preprint arXiv:math/0506513},
year = {2007}
}
Comments
LaTeX, 15 pages