Resonances for homoclinic trapped sets - Bony, Jean-Francois; Fujiie, Setsuro; Ramond, Thierry; Zerzeri, Maher (Paris : Societe Mathematique de France, 2018)
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 the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states.
Includes bibliographical references.
Keywords: Schrodinger operator; Dynamics; Asymptotes; Microlocal analysis