Fractal Weyl law for open quantum chaotic maps

Abstract : We study the semiclassical quantization of Poincaré maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
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Stéphane Nonnenmacher, Johannes Sjoestrand, Maciej Zworski. Fractal Weyl law for open quantum chaotic maps. Annals of Mathematics, Princeton University, Department of Mathematics, 2014, 179 (1), pp.179-251. ⟨10.4007/annals.2014.179.1.3⟩. ⟨hal-00593626⟩

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