Fractional monodromy in the \(1\:- 2\) resonance

DOI10.1016/j.aim.2006.05.006zbMath1107.37048OpenAlexW2037401992MaRDI QIDQ864572

Dmitrií A. Sadovskií, Richard H. Cushman, Konstantinos Efstathiou

Publication date: 12 February 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.05.006

zbMATH Keywords

monodromysingular toric fibrationLiouville integrable system

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Momentum maps; symplectic reduction (53D20) Fiberings with singularities in algebraic topology (55R55)

Related Items (13)

Dynamics near the \(p: - q\) resonance ⋮ Uncovering fractional monodromy ⋮ Parallel transport along Seifert manifolds and fractional monodromy ⋮ Rotation forms and local Hamiltonian monodromy ⋮ Global properties of integrable Hamiltonian systems ⋮ Recent advances in the monodromy theory of integrable Hamiltonian systems ⋮ The \(1:\pm 2\) resonance ⋮ Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems ⋮ Fractional monodromy: parallel transport of homology cycles ⋮ Classification of perturbations of the hydrogen atom by small static electric and magnetic fields ⋮ Wave attraction in resonant counter-propagating wave systems ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy ⋮ Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

Cites Work

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• Fractional monodromy of resonant classical and quantum oscillators
• Metamorphoses of Hamiltonian systems with symmetries
• The Poincaré-Lyapunov-Liouville-Arnol'd theorem
• Fractional monodromy: parallel transport of homology cycles
• Interpretation of quantum Hamiltonian monodromy in terms of lattice defects
• On global action-angle coordinates
• Non-Hamiltonian monodromy

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