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Article Dans Une Revue Journal of the European Mathematical Society Année : 2018

Rational invariant tori and band edge spectra for non-selfadjoint operators

Résumé

We study semiclassical asymptotics for spectra of non-selfadjoint perturbations of selfadjoint analytic $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Complete asymptotic expansions are established for all individual eigenvalues in suitable regions of the complex spectral plane, near the edges of the spectral band, coming from rational flow-invariant Lagrangian tori.

Dates et versions

hal-01737036 , version 1 (19-03-2018)

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Michael Hitrik, Johannes Sjöstrand. Rational invariant tori and band edge spectra for non-selfadjoint operators. Journal of the European Mathematical Society, 2018, 20 (2), pp.391-457. ⟨10.4171/JEMS/770⟩. ⟨hal-01737036⟩
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