PETKOV, Vesselin; STOYANOV, Luchezar

doi:10.1007/s00220-012-1419-x

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PETKOV, Vesselin
Institut de Mathématiques de Bordeaux [IMB]

STOYANOV, Luchezar
School of Mathematics and Statistics [Crawley, Perth]

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Communications in Mathematical Physics. 2012, vol. 310, n° 3, p. 675-704

Springer Verlag

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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.< Leer menos

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Distribution of periods of closed trajectories in exponentially shrinking intervals

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