Monodromy in the champagne bottle

DOI10.1007/BF00944566zbMath0755.58028MaRDI QIDQ1186488

Larry M. Bates

Publication date: 28 June 1992

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

action-angle variablescompletely integrable Hamiltonian system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (29)

An introduction to classical monodromy: Applications to molecules in external fields ⋮ Nekhoroshev's approach to Hamiltonian monodromy ⋮ Hamiltonian perturbation theory on a manifold ⋮ A note on focus-focus singularities ⋮ 2-D Duffing oscillator: elliptic functions from a dynamical systems point of view ⋮ The Euler-Poinsot top: a non-commutatively integrable system without global action-angle coordinates ⋮ Monodromy of Hamiltonian systems with complexity 1 torus actions ⋮ Hamiltonian monodromy and Morse theory ⋮ Classification of Lagrangian fibrations over a Klein bottle ⋮ Parallel transport along Seifert manifolds and fractional monodromy ⋮ Hamiltonian Monodromy via spectral Lax pairs ⋮ Rotation forms and local Hamiltonian monodromy ⋮ Almost Lagrangian obstruction ⋮ Dissipative-Hamiltonian decomposition of smooth vector fields based on symmetries ⋮ Global properties of integrable Hamiltonian systems ⋮ Recent advances in the monodromy theory of integrable Hamiltonian systems ⋮ An affine model for the actions in an integrable system with monodromy ⋮ Kolmogorov condition for integrable systems with focus-focus singularities ⋮ A semi-classical study of the Jaynes–Cummings model ⋮ Algebraic approach to two-dimensional systems: Shape phase transitions, monodromy, and thermodynamic quantities ⋮ Non-Hamiltonian monodromy ⋮ Superintegrable Hamiltonian systems: Geometry and perturbations ⋮ Topological classification of Lagrangian fibrations ⋮ Hamiltonian monodromy via geometric quantization and theta functions ⋮ No monodromy in the champagne bottle, or singularities of a superintegrable system ⋮ Monodromy in two degrees of freedom integrable systems ⋮ Unnamed Item ⋮ THE 2-D SEXTIC HAMILTONIAN OSCILLATOR ⋮ Geometric structure of ``broadly integrable Hamiltonian systems

Cites Work

• The Hamiltonian Hopf bifurcation
• Symplectic manifolds and their Lagrangian submanifolds
• Perturbations of the spherical pendulum and Abelian integrals.
• Examples for obstructions to action-angle coordinates
• Degeneration of Hamiltonian monodromy cycles
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