Groups, Geometry, and Dynamics


Full-Text PDF (213 KB) | List online-first GGD articles | GGD summary
Online access to the full text of Groups, Geometry, and Dynamics is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
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)