The Hannay angles: Geometry, adiabaticity, and an example

DOI10.1007/BF01244019zbMath0825.58012MaRDI QIDQ1812598

Simon Golin, Stefano Marmi, Andreas Knauf

Publication date: 25 June 1992

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsphase spaceHannay angles

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Two-body problems (70F05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (18)

On the geometry of slow-fast phase spaces and the semiclassical quantization ⋮ On integrable models close to slow-fast Hamiltonian systems ⋮ Contribution to the symplectic structure in the quantization rule due to noncommutativity of adiabatic parameters ⋮ On the geometric phase in the spatial equilibria of nonlinear rods ⋮ On the global structure of normal forms for slow-fast Hamiltonian systems ⋮ The tennis racket effect in a three-dimensional rigid body ⋮ Hannay angles and Grassmannian action-angle quantum states ⋮ Dynamical fluctuations in classical adiabatic processes: general description and their implications ⋮ On the classical limit of Berry's phase integrable systems ⋮ Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems ⋮ Geometric phases in the motion of rigid bodies ⋮ Unnamed Item ⋮ Geometric phases for classical and quantum dynamics: Hannay angle and Berry phase for loops on a torus ⋮ Geometric mixing ⋮ Adiabatic Berry phase and Hannay angle for open paths ⋮ Perturbed Hamiltonian dynamics from deformation of Poisson brackets ⋮ The \(n\)-centre problem of celestial mechanics for large energies ⋮ Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

Cites Work

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• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Complexity of action of reductive groups
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Quantal phase factors accompanying adiabatic changes
• Classical adiabatic angles and quantal adiabatic phase
• Classical non-adiabatic angles
• Existence of the Hannay angle for single-frequency systems
• On the adiabatic theorem for the Hamiltonian system of differential equations in the classical mechanics, I
• Averaging methods in nonlinear dynamical systems

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