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Birkhoff normal forms in semi-classical inverse problems. (English) Zbl 1258.35208

Summary: We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.

MSC:

35R30 Inverse problems for PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
81U40 Inverse scattering problems in quantum theory
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