Journal of Modern Dynamics (JMD)

Modified Schmidt games and a conjecture of Margulis

Pages: 429 - 460, Issue 3, September 2013      doi:10.3934/jmd.2013.7.429

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Dmitry Kleinbock - Goldsmith 207, Brandeis University, Waltham, MA 02454-9110, United States (email)
Barak Weiss - Ben Gurion University, Be'er Sheva, Israel 84105, Israel (email)

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.

Keywords:  Schmidt games, conjecture of Margulis, partially hyperbolic flows, homogeneous spaces.
Mathematics Subject Classification:  Primary: 11J83; Secondary: 11J54, 37A17, 37A45.

Received: December 2012;      Available Online: December 2013.