Flat trace distribution of the geodesic flow on compact hyperbolic plane

Abstract

In this paper, we establish the spectral decomposition of the Koopman operator and determine the flat-trace distribution associated with the geodesic flow on the co-circle bundle over the compactification of Poincaré upper half-plane ${\mathbf{H}}^2=\{z\in \mathbb{C}:\Im (z)>0\}$, equipped with the hyperbolic metric $d{s}^2=\frac{d{z}^2}{\Im (z{)}^2}$.

20 pages, 0 figures