Modified Schmidt games and a conjecture of Margulis

Dmitry Kleinbock; Barak Weiss

doi:10.3934/jmd.2013.7.429

Article Contents

2013, Volume 7, Issue 3: 429-460. Doi: 10.3934/jmd.2013.7.429

This issue Previous Article Winning games for bounded geodesics in moduli spaces of quadratic differentials Next Article Ergodic properties of $k$-free integers in number fields

Modified Schmidt games and a conjecture of Margulis

Dmitry Kleinbock^1, and
Barak Weiss^2,

1.
Goldsmith 207, Brandeis University, Waltham, MA 02454-9110
2.
Ben Gurion University, Be'er Sheva, Israel 84105

Received: November 30, 2012

Published: November 2013

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Abstract

We prove a conjecture of G.A. Margulis on the abundance of certain exceptional orbits of partially hyperbolic flows on homogeneous spaces by utilizing a theory of modified Schmidt games, which are modifications of $(\alpha,\beta)$-games introduced by W. Schmidt in mid-1960s.

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Mathematics Subject Classification: Primary: 11J83; Secondary: 11J54, 37A17, 37A45.

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