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.

中文翻译：

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齐次空间上发散轨迹的 Hausdorff 维数

对于有限体积均匀空间上的一个参数子组动作，我们考虑在平均轨迹上允许发散的点集。我们表明该集合的 Hausdorff 维数严格小于齐次空间的流形维数。作为推论，我们知道允许发散轨迹的点集的 Hausdorff 维数不完全，这证明了 Y. Cheung 的猜想。