Flat trace distribution of the geodesic flow on compact hyperbolic plane

Hy Lam

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arXiv · 2411.11392

Flat trace distribution of the geodesic flow on compact hyperbolic plane

Hy Lam

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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 Poincar\'e upper half-plane $\mathbf{H}^2 = \{z \in \mathbb{C} : \Im(z) > 0\}$, equipped with the hyperbolic metric $ds^2 = \frac{dz^2}{\Im(z)^2}$.

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Hy Lam. 2024-11-18. Flat trace distribution of the geodesic flow on compact hyperbolic plane. https://arxiv.org/abs/2411.11392

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