Friendly measures, homogeneous flows and singular vectors

Details Friendly measures, homogeneous flows and singular vectors Friendly measures, homogeneous flows and singular vectors

2005-06-24

arxiv.org/abs/math/0506513v1

Mathematics

Number Theory

LaTeX, 15 pages

Scientific paper

We prove that singular vectors have measure zero with respect to any friendly
measure on $\Bbb R^n$ (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.

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