We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form
here where is the dimension and is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve
for a fixed
On décrit les résonances les plus proches de l’axe réel qui sont créées, sur une variété à bouts euclidiens, par diffraction sur des singularités coniques. Ces résonances sont, asymptotiquement, régulièrement distribuées le long d’une courbe logarithmique. On montre ensuite que, sous cette courbe, il y a une région logarithmique qui ne contient aucune autre résonance de la forme
ici ; où est la dimension et la longueur de la plus longue géodésique reliant deux points coniques.
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Accepted:
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Keywords: Diffraction, conic singularities, wave propagation, scattering, resonances.
Mot clés : Diffraction, singularités coniques, propagation des ondes, diffusion, résonances.
Hillairet, Luc 1; Wunsch, Jared 2
@article{AIF_2020__70_4_1715_0, author = {Hillairet, Luc and Wunsch, Jared}, title = {On resonances generated by conic diffraction}, journal = {Annales de l'Institut Fourier}, pages = {1715--1752}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {4}, year = {2020}, doi = {10.5802/aif.3355}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3355/} }
TY - JOUR AU - Hillairet, Luc AU - Wunsch, Jared TI - On resonances generated by conic diffraction JO - Annales de l'Institut Fourier PY - 2020 SP - 1715 EP - 1752 VL - 70 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3355/ DO - 10.5802/aif.3355 LA - en ID - AIF_2020__70_4_1715_0 ER -
%0 Journal Article %A Hillairet, Luc %A Wunsch, Jared %T On resonances generated by conic diffraction %J Annales de l'Institut Fourier %D 2020 %P 1715-1752 %V 70 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3355/ %R 10.5802/aif.3355 %G en %F AIF_2020__70_4_1715_0
Hillairet, Luc; Wunsch, Jared. On resonances generated by conic diffraction. Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1715-1752. doi : 10.5802/aif.3355. https://aif.centre-mersenne.org/articles/10.5802/aif.3355/
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