COUNTING AND EQUIDISTRIBUTION OF STRONGLY REVERSIBLE CLOSED GEODESICS IN NEGATIVE CURVATURE

Abstract Let M be a pinched negatively curved Riemannian orbifold, whose fundamental group has torsion of order $2$ . 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 $T^1M$ , 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 $2$ -torsion. We give new examples in real hyperbolic Coxeter groups, complex hyperbolic orbifolds and graphs of groups.