Divergences in the iterative and perturbative methods for computing Hannays angle

A classical analog is obtained for Berrys nonperturbative scheme of adiabatic iteration which computes corrections to Berrys phase (or Hannays angle) for finite values of the adiabatic parameter . The iterative method is compared to the Lie version of adiabatic perturbation theory. Both approaches show a divergence of k!k, where k is the order of iteration. It is argued that the divergences are a mathematical artifact of the asymptotic methods used, not related to the physical effect of transitions, nor to the nonconservation of the action variables.