Hamiltonian systems with detuned 1:1:2 resonance: manifestation of bidromy

DOI10.1016/j.aop.2006.09.011zbMath1106.81082OpenAlexW1995743946MaRDI QIDQ863937

Boris I. Zhilinskiĭ, Dmitrií A. Sadovskií

Publication date: 12 February 2007

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aop.2006.09.011

zbMATH Keywords

integrable modelnonlinear resonancemolecular vibrationsbidromyquantum monodromy

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Molecular physics (81V55) Nonlinear resonances for nonlinear problems in mechanics (70K30) Monodromy on manifolds (58K10)

Related Items (15)

The harmonic Lagrange top and the confluent Heun equation ⋮ Hamiltonian Monodromy via spectral Lax pairs ⋮ Hamiltonian Hopf bifurcations near a chaotic Hamiltonian resonance ⋮ Near-resonances and detuning in classical and quantum mechanics ⋮ A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy ⋮ Global properties of integrable Hamiltonian systems ⋮ Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems ⋮ On detuned 1:1:3 Hamiltonian resonance with cases of symmetric cubic and quartic potentials ⋮ Classification of perturbations of the hydrogen atom by small static electric and magnetic fields ⋮ The coupled 1:2 resonance in a symmetric case and parametric amplification model ⋮ All relative equilibria of Hamiltonian in detuned 1:2:3 resonance ⋮ Monodromy in non-integrable systems on certain compact classical phase spaces ⋮ Bifurcations and monodromy of the axially symmetric \(1:1:-2\) resonance ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy ⋮ Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

Cites Work

• On the Hamiltonian Hopf bifurcations in the 3D Hénon-Heiles family
• Fractional Hamiltonian monodromy
• The Hamiltonian Hopf bifurcation
• Quantum monodromy in integrable systems
• Monodromy in the resonant swing spring
• Pulsation and precession of the resonant swinging spring
• Fractional monodromy of resonant classical and quantum oscillators
• Monodromy in the hydrogen atom in crossed fields
• Metamorphoses of Hamiltonian systems with symmetries
• The problem of two fixed centers: bifurcations, actions, monodromy
• Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields
• Monodromy of the quantum 1:1:2 resonant swing spring
• Linear Hamiltonian Hopf bifurcation for point–group–invariant perturbations of the 1:1:1 resonance
• Hamiltonian Monodromy as Lattice Defect
• The quantum mechanical spherical pendulum
• On global action-angle coordinates
• Quantum monodromy in the two-centre problem
• Stepwise Precession of the Resonant Swinging Spring
• Perturbations of the 1 : 1 : 1 resonance with tetrahedral symmetry: a three degree of freedom analogue of the two degree of freedom Hénon–Heiles Hamiltonian
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