Distribution of Periods of Closed Trajectories in Exponentially Shrinking Intervals
نویسنده
چکیده
For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods Tγ lying in exponentially shrinking intervals (x−e−δx, x+ e), δ > 0, x → +∞. A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hyperbolic flows on basic sets, in particular to geodesic flows on manifolds of constant negative curvature and to open billiard flows.
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