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arXiv · 2505.07738

Counting and equidistribution of strongly reversible closed geodesics in negative curvature

Jouni Parkkonen·Frédéric Paulin
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Abstract

Let $M$ be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order $2$. Generalizing 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 $M$, and prove their equidistribution towards the Bowen-Margulis measure. The result is proved in the more general setting with weights coming from thermodynamic formalism, and also in the analogous setting of graphs of groups with $2$-torsion. We give new examples in real hyperbolic Coxeter groups, complex hyperbolic orbifolds and graphs of groups.

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Jouni Parkkonen, Frédéric Paulin. 2025-05-12. Counting and equidistribution of strongly reversible closed geodesics in negative curvature. https://arxiv.org/abs/2505.07738

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