Fractal Weyl law for open quantum chaotic maps

Details Fractal Weyl law for open quantum chaotic maps Fractal Weyl law for open quantum chaotic maps

2011-05-16

arxiv.org/abs/1105.3128v1

Mathematics

Analysis of PDEs

69 pages, 7 figures

Scientific paper

We study the semiclassical quantization of Poincar\'e 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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