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In the framework of semiclassical resonances, we make more precise the link between polynomial estimates of the extension of the resolvent and propagation of the singularities through the trapped set. This approach makes it possible to eliminate infinity and to concentrate the study near the trapped set. It has allowed us in previous papers to obtain the asymptotic of resonances in various geometric situations.
We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of th
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 obt
We investigate plasmon resonances for curved nanorods which present anisotropic geometries. We analyze quantitative properties of the plasmon resonance and its relationship to the metamaterial configurations and the anisotropic geometries of the nano
Let (X_R, 0) be a germ of real analytic subset in (R^N, 0) of pure dimension n+1 with an isolated singularity at 0. Let (f_R,0) : (X_R, 0) --> (R,0) a real analytic germ with an isolated singularity at 0, such that its complexification f_C vanishes o
We prove that for the Martinet wave equation with flat metric, which a subelliptic wave equation, singularities can propagate at any speed between 0 and 1 along any singular geodesic. This is in strong contrast with the usual propagation of singulari