Let G be a semisimple real algebraic group defined over ${\mathbb {Q}}$ , $\Gamma $ be an arithmetic subgroup of G, and T be a maximal ${\mathbb {R}}$ -split torus. A trajectory in $G/\Gamma $ is divergent if eventually it leaves every compact subset. In some cases there is a finite collection of explicit algebraic data which accounts for the divergence. If this is the case, the divergent trajectory is called obvious. Given a closed cone in T, we study the existence of non-obvious divergent trajectories under its action in $G\kern-1pt{/}\kern-1pt\Gamma $ . We get a sufficient condition for the existence of a non-obvious divergence trajectory in the general case, and a full classification under the assumption that $\mathrm {rank}_{{\mathbb {Q}}}G=\mathrm {rank}_{{\mathbb {R}}}G=2$ .

中文翻译：

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有理二阶算术齐次空间中的发散轨迹

让G是一个半单实数代数群，定义在${\mathbb {Q}}$,$\伽马$是一个算术子群G， 和吨成为最大的${\mathbb {R}}$-分裂环面。中的轨迹$G/\伽玛 $如果最终离开每个紧凑子集，则它是发散的。在某些情况下，存在一个有限的显式代数数据集合，它解释了分歧。如果是这种情况，则称发散轨迹是明显的。给定一个封闭的圆锥吨，我们研究了在其作用下非明显发散轨迹的存在$G\kern-1pt{/}\kern-1pt\Gamma $. 我们得到了在一般情况下存在非明显发散轨迹的充分条件，以及在假设下的完整分类$\mathrm {秩}_{{\mathbb {Q}}}G=\mathrm {秩}_{{\mathbb {R}}}G=2$.