# Semiclassical resonances associated with a periodic orbit

2 CPT - E8 Dynamique quantique et analyse spectrale
CPT - Centre de Physique Théorique - UMR 7332
Abstract : We consider in this Note resonances for a $h$-Pseudo-Differential Operator $H(x,hD_x;h)$ on $L^2(M)$ induced by a periodic orbit of hyperbolic type, as arises for Schr\"odinger operator with AC Stark effect when $M={\bf R}^n$, or the geodesic flow on an axially symmetric manifold $M$, extending Poincar\'e example of Lagrangian systems with 2 degrees of freedom. We generalize the framework of [G\'eSj], in the sense that we allow for hyperbolic and elliptic eigenvalues of Poincar\'e map, and look for so-called semi-excited resonances with imaginary part of magnitude $-h\log h$, or $h^s$, with \$0
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01591920
Contributor : Stéphanie Suciu <>
Submitted on : Friday, September 22, 2017 - 11:39:23 AM
Last modification on : Thursday, March 15, 2018 - 4:56:08 PM

### Citation

Hanen Louati, Michel Rouleux. Semiclassical resonances associated with a periodic orbit. Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2016, 100 (5-6), pp.724-730. ⟨10.1134/S0001434616110092⟩. ⟨hal-01591920⟩

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