Work

Counting and Equidistribution of Strongly Reversible Closed Geodesics in Negative Curvature

Year: 2026

Type: article

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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748026101662

Authors: Jouni Parkkonen, Frédéric Paulin

Institutions: University of Jyväskylä, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Centre National de la Recherche Scientifique