Friendly measures, homogeneous flows and singular vectors | Zendy

Dmitry Kleinbock | Zendy; Barak Weiss | Zendy

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Friendly measures, homogeneous flows and singular vectors

Author(s) -

Dmitry Kleinbock,

Barak Weiss

Publication year - 2005

Publication title -

contemporary mathematics - american mathematical society

Language(s) - English

Resource type - Reports

SCImago Journal Rank - 0.106

H-Index - 12

eISSN - 1098-3627

pISSN - 0271-4132

DOI - 10.1090/conm/385/07201

Subject(s) - mathematics , measure (data warehouse) , homogeneous , submanifold , homogeneous polynomial , pure mathematics , mathematical analysis , zero (linguistics) , polynomial , combinatorics , matrix polynomial , data mining , computer science , linguistics , philosophy

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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