Fractional monodromy of resonant classical and quantum oscillators

DOI10.1016/S1631-073X(02)02584-0zbMath1017.81009OpenAlexW2063383779MaRDI QIDQ1565915

Boris I. Zhilinskiĭ, Dmitrií A. Sadovskií, Nikolaiĭ N. Nekhoroshev

Publication date: 27 May 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1631-073x(02)02584-0

zbMATH Keywords

class of integrable fibrationsnonlinear oscillator systems

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Monodromy on manifolds (58K10)

Related Items (15)

Nekhoroshev's approach to Hamiltonian monodromy ⋮ Hamiltonian systems with detuned 1:1:2 resonance: manifestation of bidromy ⋮ Fractional monodromy in the \(1\:- 2\) resonance ⋮ Dynamics near the \(p: - q\) resonance ⋮ Uncovering fractional monodromy ⋮ Global properties of integrable Hamiltonian systems ⋮ Energy bands: Chern numbers and symmetry ⋮ The \(1:\pm 2\) resonance ⋮ Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems ⋮ Monodromy of the quantum 1:1:2 resonant swing spring ⋮ Fractional monodromy: parallel transport of homology cycles ⋮ Interpretation of quantum Hamiltonian monodromy in terms of lattice defects ⋮ Classification of perturbations of the hydrogen atom by small static electric and magnetic fields ⋮ Monodromy in non-integrable systems on certain compact classical phase spaces ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy

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