Groups, Geometry, and Dynamics


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Published online first: 2021-08-04
DOI: 10.4171/GGD/624

Narrow equidistribution and counting of closed geodesics on noncompact manifolds

Barbara Schapira[1] and Samuel Tapie[2]

(1) Université de Rennes 1, France
(2) Université de Nantes, France

We prove the equidistribution of (weighted) periodic orbits for the geodesic flow on noncompact negatively curved manifolds toward equilibrium states in the narrow topology, i.e. in the dual of bounded continuous functions. We deduce an exact asymptotic counting for periodic orbits (weighted or not), which was previously known only for geometrically finite manifolds.

Keywords: Negative curvature, geodesic flow, periodic orbits, equidistribution, Gibbs measure, counting

Schapira Barbara, Tapie Samuel: Narrow equidistribution and counting of closed geodesics on noncompact manifolds. Groups Geom. Dyn. Electronically published on August 4, 2021. doi: 10.4171/GGD/624 (to appear in print)