Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point

Hitrik, Michael ; Sjöstrand, Johannes

Canadian journal of mathematics, Tome 60 (2008) no. 3, pp. 572-657

Résumé

This is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint $h$ -pseudodifferential operators in dimension 2, having a periodic classical flow. Assuming that the strength $\epsilon$ of the perturbation is in the range ${{h}^{2}}\ll \epsilon \ll {{h}^{1/2}}$ (and may sometimes reach even smaller values), we get an asymptotic description of the eigenvalues in rectangles $[-1/C,1/C]+i\epsilon [{{F}_{0}}-1/C,{{F}_{0}}+1/C],C\gg 1$ , when $\epsilon {{F}_{0}}$ is a saddle point value of the flow average of the leading perturbation.

Détail

DOI : 10.4153/CJM-2008-028-3

Mots-clés : 31C10, 35P20, 35Q40, 37J35, 37J45, 53D22, 58J40, non-selfadjoint, eigenvalue, periodic flow, branching singularity

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