Friendly measures, homogeneous flows and singular vectors

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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.
LaTeX, 15 pages

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Number Theory, Dynamical Systems, 11J83; 37A13

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http://salesiana.dossiersoluciones.com/handle/123456789/75584

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506513
 http://arxiv.org/abs/math/0506513

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arXiv