English

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 Rn\Bbb R^n (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.

Keywords

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