Higher index focus-focus singularities in the Jaynes-Cummings-Gaudin model: symplectic invariants and monodromy

DOI10.1016/j.geomphys.2014.07.011zbMath1314.53133arXiv1312.6087OpenAlexW2962892870MaRDI QIDQ478595

O. Babelon, Benoit Douçot

Publication date: 3 December 2014

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6087

zbMATH Keywords

Poisson bracketsspinharmonic oscillator

Mathematics Subject Classification ID

Related Items (9)

Generating hyperbolic singularities in semitoric systems via Hopf bifurcations ⋮ Taylor series and twisting-index invariants of coupled spin-oscillators ⋮ Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems ⋮ Hamiltonian Monodromy via spectral Lax pairs ⋮ Elliptic three-boson system, ``two-level three-mode JCD-type models and non-skew-symmetric classical r-matrices ⋮ Characterization of toric systems via transport costs ⋮ From compact semi-toric systems to Hamiltonian \(S^1\)-spaces ⋮ Integrability and correspondence of classical and quantum non-linear three-mode systems ⋮ Classifying toric and semitoric fans by lifting equations from \(\mathrm{SL}_2(\mathbb{Z})\)

Cites Work

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• Semi-global symplectic invariants of the Euler top
• Symplectic invariants near hyperbolic-hyperbolic points
• Hamiltonian dynamics and spectral theory for SPIN-oscillators
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Hamiltonian monodromy via Picard-Lefschetz theory
• On semi-global invariants for focus-focus singularities
• Classical Bethe ansatz and normal forms in an integrable version of the Dicke model
• On global action-angle coordinates

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