On the almost sure spiraling of geodesics in negatively curved manifolds
On the almost sure spiraling of geodesics in negatively curved manifolds
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关于负曲流形中测地线几乎肯定的螺旋
DOI：
10.4310/jdg/1287580966
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
F. Paulin
中科院分区：
文献类型：
--
作者：
Sa’ar Hersonsky;F. Paulin
给定负弯曲测地度量空间$M$，我们研究了$M$的(局部)测地线在点的小邻域内的统计渐近穿透行为、闭测地线的统计渐近穿透行为以及$M$的其他紧凸子集的统计渐近穿透行为.我们证明了Khintchine型和对数律型关于这些对象周围的测地线螺旋化的结果。作为结果，在树环境下，我们得到了非阿基米德局域场元素的丢番图二次无理逼近结果。
Given a negatively curved geodesic metric space $M$, we study the statistical asymptotic penetration behavior of (locally) geodesic lines of $M$ in small neighborhoods of points, of closed geodesics, and of other compact (locally) convex subsets of $M$. We prove Khintchine-type and logarithme law-type results for the spiraling of geodesic lines around these objets. As a consequence in the tree setting, we obtain Diophantine approximation results of elements of non-archimedian local fields by quadratic irrational ones.