COUNTING AND EQUIDISTRIBUTION OF STRONGLY REVERSIBLE CLOSED GEODESICS IN NEGATIVE CURVATURE
Abstract
Abstract Let M be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order 2 $2$ 2 . Generalising results of Sarnak and Erlandsson-Souto for constant curvature oriented surfaces, and with very different techniques, we give an asymptotic counting result on the number of strongly reversible periodic orbits of the geodesic flow in T 1 M $T^1M$ upper T Superscript 1 Baseline upper M , and prove their equidistribution towards the Bowen-Margulis measure. The result holds in the more general setting with weights coming from thermodynamic formalism, and also in the analogous setting of graphs of groups with 2 $2$ 2 -torsion. We give new examples in real hyperbolic Coxeter groups, complex hyperbolic orbifolds and graphs of groups.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 4
- Pages
- 1921–1959
- Publication date
- 19 May 2026
- Language
- EN