Singular Bohr-Sommerfeld Rules for 2D Integrable Systems

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dc.creatorde Verdiere, Yves Colin
dc.creatorNgoc, San Vu
dc.date2000-05-26
dc.date.accessioned2026-07-07T04:35:34Z
dc.date.available2026-07-07T04:35:34Z
dc.descriptionIn this paper, we describe Bohr-Sommerfeld rules for semi-classical completely integrable systems with 2 degrees of freedom with non degenerate singularities (Morse-Bott singularities) under the assumption that the energy level of the first Hamiltonian is non singular. The more singular case of {\it focus-focus} singularities is studied in [Vu Ngoc San, CPAM 2000] and [Vu Ngoc San, PhD 1998] The case of 1 degree of freedom has been studied in [Colin de Verdiere-Parisse, CMP 1999] Our theory is applied to some famous examples: the geodesics of the ellipsoid, the $1:2$-resonance, and Schroedinger operators on the sphere $S^2$. A numerical test shows that the semiclassical Bohr-Sommerfeld rules match very accurately the ``purely quantum'' computations.
dc.descriptionpostscript, 61 pages, figures best seen in color. Preprint Institut Fourier
dc.identifierhttps://arxiv.org/abs/math/0005264
dc.identifierhttp://arxiv.org/abs/math/0005264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59293
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subjectSpectral Theory
dc.subject34E20; 34L25; 81Q20; 58F07; 58C40; 58C27
dc.titleSingular Bohr-Sommerfeld Rules for 2D Integrable Systems
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