Singular Bohr–Sommerfeld rules for 2D integrable systems

DOI10.1016/S0012-9593(03)00002-8zbMath1028.81026arXivmath/0005264MaRDI QIDQ4707074

San Vũ Ngoc, Yves Colin de Verdière

Publication date: 9 June 2003

Published in: Annales Scientifiques de lʼÉcole Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005264

zbMATH Keywords

numerical testfocus-focus singularitiesnondegenerate singularitiesMorse-Bott singularitiessemiclassical completely integrable systems

Mathematics Subject Classification ID

Groups and algebras in quantum theory and relations with integrable systems (81R12) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (19)

Singular Lagrangian manifolds and semiclassical analysis. ⋮ Pointwise bounds for joint eigenfunctions of quantum completely integrable systems ⋮ Uncovering fractional monodromy ⋮ Actions toriques et groupes d'automorphismes de singularités des systèmes dynamiques intégrables. (Torus actions and automorphism groups of singularities of integrable dynamical systems) ⋮ Integrable systems and group actions ⋮ Energy bands: Chern numbers and symmetry ⋮ Observability and quantum limits for the Schrödinger equation on 𝕊^{𝕕} ⋮ Critical loci for Higgs bundles ⋮ Spectral asymptotics via the semiclassical Birkhoff normal form ⋮ Integrable systems, symmetries, and quantization ⋮ Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems ⋮ Monodromy of the quantum 1:1:2 resonant swing spring ⋮ Interpretation of quantum Hamiltonian monodromy in terms of lattice defects ⋮ Intersections of Lagrangian submanifolds and the Mel'nikov 1-form ⋮ Symplectic theory of completely integrable Hamiltonian systems ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems ⋮ Riemannian manifolds with maximal eigenfunction growth ⋮ Integrability, normal forms, and magnetic axis coordinates

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