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Friendly measures, homogeneous flows and singular vectors

Research paper by Dmitry Kleinbock, Barak Weiss

Indexed on: 24 Jun '05Published on: 24 Jun '05Published in: Mathematics - Number Theory



Abstract

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.