Abstract
The Hannay angles were introduced by Hannay as a means of measuring a holonomy effect in classical mechanics closely corresponding to the Berry phase in quantum mechanics. Using parameter-dependent momentum mappings we show that the Hannay angles are the holonomy of a natural connection. We generalize this effect to non-Abelian group actions and discuss non-integrable Hamiltonian systems. We prove an averaging theorem for phase space functions in the case of general multi-frequency dynamical systems which allows us to establish the almost adiabatic invariance of the Hannay angles. We conclude by giving an application to celestial mechanics.
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Communicated by A. Jaffe
Supported by the Deutsche Forschungsgemeinschaft
Supported by the Akademie der Wissenschaften zu Berlin
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Golin, S., Knauf, A. & Marmi, S. The Hannay angles: Geometry, adiabaticity, and an example. Commun.Math. Phys. 123, 95–122 (1989). https://doi.org/10.1007/BF01244019
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DOI: https://doi.org/10.1007/BF01244019