On integrable models close to slow-fast Hamiltonian systems

DOI10.1134/S1995080222040059zbMath1494.70002OpenAlexW4226505911WikidataQ114074830 ScholiaQ114074830MaRDI QIDQ2140897

Yanyan Li

Publication date: 23 May 2022

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080222040059

zbMATH Keywords

averaging methodintegrable modelnormal form theory\( \mathbb{S}^1 \)-actionsimproved first integralslow-fast Hamiltonian system

Mathematics Subject Classification ID

General perturbation schemes for nonlinear problems in mechanics (70K60) Hamilton's equations (70H05) Symplectic geometry, contact geometry (53Dxx) Systems with slow and fast motions for nonlinear problems in mechanics (70K70) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Cites Work

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• Contribution to the symplectic structure in the quantization rule due to noncommutativity of adiabatic parameters
• Homological equations for tensor fields and periodic averaging
• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• Differential geometric methods in mathematical physics. (Proceedings of the XIth Annual Conference on Differential Geometric Methods in Mathematical Physics, held in Jerusalem, August 5-11, 1982)
• On the geometry of slow-fast phase spaces and the semiclassical quantization
• On the change in the adiabatic invariant on crossing a separatrix in systems with two degrees of freedom
• The Hannay angles: Geometry, adiabaticity, and an example
• Geometric phases in classical and quantum mechanics
• Reduction, symmetry, and phases in mechanics
• Classical non-adiabatic angles
• The elastic pendulum: A nonlinear paradigm
• On mechanisms of destruction of adiabatic invariance in slow–fast Hamiltonian systems
• Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems
• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems