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Modified Schmidt games and a conjecture of Margulis

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


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