Geodesic
Fractal Weyl law for open quantum chaotic maps
Stéphane Nonnenmacher1 ; Johannes Sjöstrand2 ; Maciej Zworski3
1 Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, CEA-Saclay, Gif-sur-Yvette, France
2 Institut de Mathématiques de Bourgogne, Université de Bourgogne, UFR Science et Techniques, Dijon Cedex, France
3 University of California at Berkeley, Berkeley, CA
Annals of mathematics, Tome 179 (2014) no. 1, pp. 179-251.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2014.179.1.3

Stéphane Nonnenmacher 1 ; Johannes Sjöstrand 2 ; Maciej Zworski 3

1 Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, CEA-Saclay, Gif-sur-Yvette, France
2 Institut de Mathématiques de Bourgogne, Université de Bourgogne, UFR Science et Techniques, Dijon Cedex, France
3 University of California at Berkeley, Berkeley, CA 
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     title = {Fractal {Weyl} law for open quantum chaotic maps},
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Stéphane Nonnenmacher; Johannes Sjöstrand; Maciej Zworski. Fractal Weyl law for open quantum chaotic maps. Annals of mathematics, Tome 179 (2014) no. 1, pp. 179-251. doi : 10.4007/annals.2014.179.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.179.1.3/

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