# Narrow equidistribution and counting of closed geodesics on noncompact manifolds

## TL;DR

This paper proves the equidistribution of weighted periodic geodesic orbits on noncompact negatively curved manifolds and derives precise asymptotic counts, extending previous results beyond geometrically finite cases.

## Contribution

It establishes the first equidistribution and counting results for periodic geodesics on a broad class of noncompact manifolds, using narrow topology techniques.

## Key findings

- Weighted periodic orbits equidistribute toward equilibrium states.
- Exact asymptotic counting formulas for periodic orbits.
- Extension of counting results to non-geometrically finite manifolds.

## 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.