NDLI: An ‘almost all versus no’ dichotomy in homogeneous dynamics and Diophantine approximation

Content Provider	Semantic Scholar
Author	Kleinbock, Dmitry
Copyright Year	2009
Abstract	Let Y0 be a not very well approximable m × n matrix, and let ${\mathcal {M}}$ be a connected analytic submanifold in the space of m × n matrices containing Y0. Then almost all ${Y \in \mathcal {M}}$ are not very well approximable. This and other similar statements are cast in terms of properties of certain orbits on homogeneous spaces and deduced from quantitative nondivergence estimates for'quasi-polynomial' flows on the space of lattices.
Starting Page	205
Ending Page	218
Page Count	14
File Format	PDF HTM / HTML
DOI	10.1007/s10711-010-9477-8
Volume Number	149
Alternate Webpage(s)	https://page-one.springer.com/pdf/preview/10.1007/s10711-010-9477-8
Alternate Webpage(s)	http://arxiv.org/pdf/0904.1614v2.pdf
Alternate Webpage(s)	http://people.brandeis.edu/~kleinboc/Pub/mumbainewest.pdf
Alternate Webpage(s)	http://people.brandeis.edu/~kleinboc/Pub/mumbaifinal.pdf
Alternate Webpage(s)	http://people.brandeis.edu/~kleinboc/Pub/mumbayfinal.pdf
Alternate Webpage(s)	https://arxiv.org/pdf/0904.1614v2.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s10711-010-9477-8
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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An ‘almost all versus no’ dichotomy in homogeneous dynamics and Diophantine approximation