Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2

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dc.creatorHitrik, Michael
dc.creatorSjoestrand, Johannes
dc.date2007-03-13
dc.date.accessioned2026-07-07T07:51:52Z
dc.date.available2026-07-07T07:51:52Z
dc.descriptionWe study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable window in the complex spectral plane, provided that the strength of the non-selfadjoint perturbation $\gg h$ (or sometimes $\gg h^2$) is not too large.
dc.description66 pages
dc.identifierhttps://arxiv.org/abs/math/0703394
dc.identifierhttp://arxiv.org/abs/math/0703394
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125675
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject35P15, 35P20, 37J35, 37J40, 53D22, 58J40, 70H08
dc.titleRational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2
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