Diophantine tori and nonselfadjoint inverse spectral problems

Michael A. Hall

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arXiv · 1001.5132

Diophantine tori and nonselfadjoint inverse spectral problems

Michael A. Hall

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Abstract

We study a semiclassical inverse spectral problem based on a spectral asymptotics result of arXiv:math/0502032, which applies to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. The eigenvalues in a suitable complex window have an expansion in terms of a quantum Birkhoff normal form for the operator near several Lagrangian tori which are invariant under the classical dynamics and satisfy a Diophantine condition. In this work we prove that the normal form near a single Diophantine torus is uniquely determined by the associated eigenvalues. We also discuss the normalization procedure and symmetries of the quantum Birkhoff normal form near a Diophantine torus.

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BibTeX RIS

Michael A. Hall. 2012-12-14. Diophantine tori and nonselfadjoint inverse spectral problems. https://arxiv.org/abs/1001.5132

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