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

Published online by Cambridge University Press:  20 November 2018

Michael Hitrik  and
Johannes Sjöstrand
Michael Hitrik
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A. e-mail:, hitrik@math.ucla.edu
Johannes Sjöstrand
Affiliation:
Centre de Mathématiques, École Polytechnique, FR 91128 Palaiseau France e-mail:, johannes@math.polytechnique.fr
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Abstract

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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.

Keywords

31C1035P2035Q4037J3537J4553D2258J40non-selfadjointeigenvalueperiodic flowbranching singularity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 3 , 01 June 2008 , pp. 572 - 657
Copyright
Copyright © Canadian Mathematical Society 2008

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