Singular systems of linear forms and non-escape of mass in the space of lattices

Система будет остановлена для регулярного обслуживания. Пожалуйста, сохраните рабочие данные и выйдите из системы.

dc.contributor.author	Kadyrov, Shirali
dc.contributor.author	Kleinbock, D.
dc.contributor.author	Lindenstrauss, E.
dc.contributor.author	Margulis, G.A.
dc.date.accessioned	2015-12-25T06:34:06Z
dc.date.available	2015-12-25T06:34:06Z
dc.date.issued	2014
dc.identifier.citation	Kadyrov Shirali, Kleinbock D., Lindenstrauss E., Margulis G.A.; 2014; Singular systems of linear forms and non-escape of mass in the space of lattices	ru_RU
dc.identifier.uri	http://nur.nu.edu.kz/handle/123456789/975
dc.description.abstract	Singular systems of linear forms were introduced by Khintchine in the 1920s, and it was shown by Dani in the 1980s that they are in one-to-one correspondence with certain divergent orbits of oneparameter diagonal groups on the space of lattices. We give a (conjecturally sharp) upper bound on the Hausdor dimension of the set of singular systems of linear forms (equivalently the set of lattices with divergent trajectories) as well as the dimension of the set of lattices with trajectories `escaping on average' (a notion weaker than divergence). This extends work by Cheung, as well as by Chevallier and Cheung. Our method di ers considerably from that of Cheung and Chevallier, and is based on the technique of integral inequalities developed by Eskin, Margulis and Mozes.	ru_RU
dc.language.iso	en	ru_RU
dc.subject	Research Subject Categories::MATHEMATICS	ru_RU
dc.subject	lattices	ru_RU
dc.title	Singular systems of linear forms and non-escape of mass in the space of lattices	ru_RU
dc.type	Article	ru_RU