Narrow equidistribution and counting of closed geodesics on noncompact manifolds

2019/07/25 by Barbara Schapira, Schapira, Barbara, Samuel Tapie +1
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS

paper · pdf · doi:10.48550/arxiv.1907.10898

arxiv created 2019/07/25 · arxiv updated 2019/07/26

Abstract

We prove the equidistribution of (weighted) periodic orbits of the geodesic ow 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 nite manifolds.

Related

• Counting closed geodesics on rank one manifolds
• Counting and equidistribution of strongly reversible closed geodesics in negative curvature
• Ergodicity and equidistribution in strictly convex Hilbert geometry
• Equidistribution and counting under equilibrium states in negative curvature and trees. Applications to non-Archimedean Diophantine approximation
• On the equidistribution of closed geodesics and geodesic nets