Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of Asymptotically Hyperbolic Manifolds   We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1)
dimensional manifolds with negative (but not necessarily constant) sectional
curvatures which equates the renormalized wave trace to the lengths of closed
geodesics. A corollary of this dynamical trace formula is a dynamical
resonance-wave trace formula for compact perturbations of convex co-compact
hyperbolic manifolds which we use to prove a growth estimate for the length
spectrum counting function. We next define a dynamical zeta function and prove
its analyticity in a half plane. In our main result, we produce a prime orbit
theorem for the geodesic flow. This is the first such result for manifolds
which have neither constant curvature nor finite volume. As a corollary to the
prime orbit theorem, using our dynamical resonance-wave trace formula, we show
that the existence of pure point spectrum for the Laplacian on negatively
curved compact perturbations of convex co-compact hyperbolic manifolds is
related to the dynamics of the geodesic flow.

8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th