Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems

In Phys. Rev. Lett. {\bf 66}, 847 (1991), T. B. Kepler and M. L. Kagan derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show that the converse is also true, namely, this geometric phase can be identified with the classical mechanical Hannay angle in an extended phase space. Our results suggest that this phase can be generalized to a stochastic evolution with an additional noise term in evolution equations.