Fractal Weyl law for open quantum chaotic maps

• Autores: Stéphane Nonnenmacher, Johannes Sjöstrand, Maciej Zworski
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 179, Nº 1, 2014, págs. 179-251
• Idioma: inglés
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• Resumen

  • We study a 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 includes the case of several convex (hard) obstacles satisfying a no-eclipse condition