Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distribution of periods of closed trajectories in exponentially
  shrinking intervals   We examine the asymptotics of the number of the closed trajectories $\gamma$
of hyperbolic flows $\phi_t$ whose primitive periods $T_{\gamma}$ lie in
exponentially shrinking intervals $(x - e^{-\delta x}, x + e^{-\delta
x}),\:\delta > 0,\: x \to + \infty.$ Our results holds for hyperbolic dynamical
systems having a symbolic model with a non-lattice roof function $f$ under the
assumption that the corresponding Ruelle operator related to $f$ satisfies
strong spectral estimates. In particular, our analysis works for open billiard
systems and for the geodesics flow on manifolds with constant negative
curvature.

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The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph