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Fractal Weyl law for open quantum chaotic maps (1105.3128v1)
Published 16 May 2011 in math.AP, math.DS, and nlin.CD
Abstract: 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.