Barrier-top resonances for non globally analytic potentials
  We give the semiclassical asymptotic of barrier-top resonances for Schr\"{o}dinger operators on ${\mathbb R}^{n}$, $n \geq 1$, whose potential is $C^{\infty}$ everywhere and analytic at infinity. In the globally analytic setting, this has already been obtained. Our proof is based on a propagation of singularities theorem at a hyperbolic fixed point that we establish here. This last result refines a theorem of the same authors, and its proof follows another approach. 
Jean-Francois Bony, Setsuro Fujiie, Thierry Ramond, Maher Zerzeri
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