Abstract: Consider the flow F_t induced by the one parameter subgroup diag(e^t,e^t,e^{-2t}) acting on X=SL(3,R)/SL(3,Z) by left multiplication. In this talk, we show that F_t admits divergent trajectories that exit to infinity at arbitrarily slow prescribed rates, answering a question of A.N. Starkov. (More precisely, let P:X-->R_{\ge0} be any proper function. Then the main result asserts that given any function U(t)-->infty as t\to\infty there exists x in X such that P(F_t(x))< U(t) for all sufficiently large t.)