Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Han, Xiaolong Hans, Yang, Bohan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204933594