  For one parameter subgroup action on a finite volume homogeneous space, we
consider the set of points admitting divergent on average trajectories. We show
that the Hausdorff dimension of this set is strictly less than the manifold
dimension of the homogeneous space. As a corollary we know that the Hausdorff
dimension of the set of points admitting divergent trajectories is not full,
which proves a conjecture of Y. Cheung.
