Fractal Weyl law for open quantum chaotic maps


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.


Stéphane Nonnenmacher

Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, CEA-Saclay, Gif-sur-Yvette, France

Johannes Sjöstrand

Institut de Mathématiques de Bourgogne, Université de Bourgogne, UFR Science et Techniques, Dijon Cedex, France

Maciej Zworski

University of California at Berkeley, Berkeley, CA