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Dynamics and zeta functions on conformally compact manifolds
In this note, we study the dynamics and associated zeta functions of
conformally compact manifolds with variable negative sectional curvatures. We
begin with a discussion of a larger class of manifolds known as convex
co-compact manifolds with variable negative curvature. Applying results from
dynamics on these spaces, we obtain optimal meromorphic extensions of weighted
dynamical zeta functions and asymptotic counting estimates for the number of
weighted closed geodesics. A meromorphic extension of the standard dynamical
zeta function and the prime orbit theorem follow as corollaries. Finally, we
investigate interactions between the dynamics and spectral theory of these
spaces
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