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Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2

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Author

Summary, in English

For a class of non-selfadjoint h-pseudodifferential operators in dimension 2, we determine all eigenvalues in an h-independent domain in the complex plane and show that they are given by a Bohr-Sommerfeld quantization condition. No complete integrability is assumed, and as a geometrical step in our proof, we get a KAM-type theorem (without small divisors) in the complex domain.

Publishing year

2003

Language

English

Pages

181-244

Publication/Series

Astérisque

Volume

284

Document type

Journal article

Publisher

SMF

Topic

  • Mathematics

Keywords

  • Bohr
  • Sommerfeld
  • eigenvalue
  • Cauchy-Riemann equation
  • torus

Status

Published

ISBN/ISSN/Other

  • ISSN: 0303-1179