Nondense orbits of flows on homogeneous spaces
Nondense orbits of flows on homogeneous spaces
复制标题
均匀空间上的非稠密流动轨道
DOI：
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发表时间：
1998
影响因子：
0.9
通讯作者：
D. Kleinbock
中科院分区：
文献类型：
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作者：
D. Kleinbock
设$F$是单模李群$G$的非拟单幂单参数（循环）子群，$\Gamma$是$G$的离散子群。我们证明了对于齐次空间$G/\Gamma$的子集$Z$, $G/\Gamma$中$F$轨道远离$Z$的点的集合具有充分的Hausdorff维数。由此导出了在常负曲率流形上测地线流的应用。
Let $F$ be a nonquasi-unipotent one-parameter (cyclic) subgroup of a unimodular Lie group $G$, $\Gamma$ a discrete subgroup of $G$. We prove that for certain classes of subsets $Z$ of the homogeneous space $G/\Gamma$, the set of points in $G/\Gamma$ with $F$-orbits staying away from $Z$ has full Hausdorff dimension. From this we derive applications to geodesic flows on manifolds of constant negative curvature.