  Several proposals aimed at measuring the Electric Dipole Moment (EDM) for
charged particles require very precise simulations and understanding of the
systematic errors that can contribute to a spin buildup mimicking the EDM
signal to be detected. In what follows, one used the
Bogoliubov-Krylov-Mitropolski method of averages to solve the T-BMT equation
and calculate the Berry phases arising for a proton EDM storage ring. The
formalism employed proved to be particularly useful to determine the evolution
of the spin at the observation point, i.e. at the location of the polarimeter.
Several selected cases of lattice imperfections were simulated and benchmarked
with the analytical estimates. This allowed the proof of the convergence of the
numerical simulations and helped gain better understanding of the systematic
errors.
