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

Hausdorff dimension of divergent trajectories on homogeneous space