Existence of the Hannay angle for single-frequency systems

Abstract

The Hannay angle was introduced by Hannay (1985) as a means of measuring an anholonomy effect in classical mechanics closely corresponding to Berry's phase in quantum mechanics. Such classical adiabatic angle shifts, the Hannay angles, arise when an integrable classical Hamiltonian involves time-dependent parameters which undergo a closed adiabatic excursion. In this paper two proofs of an averaging type of theorem for a single-frequency dynamical system are given. As a consequence one can establish the existence of the Hannay angle for a class of smooth classical Hamiltonian systems with one degree of freedom. Moreover, a review of the rotated rotator illustrates the usefulness of the averaging theorem.