Classical adiabatic holonomy and its canonical structure

In this paper we introduce some mathematical tools to further study the classical adiabatic holo- nomy effect known as Hannay’s angle. In particular, we prove with purely classical methods that the area (or angle) two-form associated with this effect can be seen as a modification of the symplectic structure of the slow-variable dynamics. We also show that, as in the quantum case, degeneracies cause singularities in this two-form. We conclude with some considerations concerning the triviality or nontriviality of the phase-space bundle associated with this phenomenon.