闭双曲3-流形中简单闭测地线的增长
Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds
- Fudan University（复旦大学）
- Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
- Research Institute of Intelligent Complex Systems, Fudan University（复旦大学复杂系统智能研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对闭双曲3-流形，研究其本原简单闭测地线数目随长度的增长规律，得出长度不超过L的该类测地线数目为e^((2+o(1))L)的结论
AI中文摘要：
设M为闭双曲3-流形，我们证明当L→∞时，长度不超过L的本原简单闭测地线数目为e^((2+o(1))L)
英文摘要：
Let $M$ be a finite-volume hyperbolic $d$-manifold with $d\ge3$. We prove that the number of primitive nonsimple closed geodesics has exponential growth rate strictly smaller than $d-1$. Consequently, asymptotically almost every primitive closed geodesic in $M$ is simple. In contrast, we show that on an arithmetic hyperbolic manifold of type~I, the unit vectors tangent to nonsimple closed geodesics are dense in the unit tangent bundle.
