Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces (Q807756)

It is shown that if G is a semisimple algebraic group defined over Q and \(\Gamma\) is an arithmetic lattice in \(G:=G_ R\) with respect to the Q- structure, then there exists a compact subset C of G/\(\Gamma\) such that, for any unipotent one-parameter subgroup \(\{u_ t\}\) of G and any \(g\in G\), the time spent in C by the \(\{u_ t\}\)-trajectory of \(g\Gamma\), during the time interval [0,T], is asymptotic to T, unless \(\{g^{- 1}u_ tg\}\) is contained in a Q-parabolic subgroup of G.