Save the third adiabatic invariants of motion in the equatorial plane magnetic field with a weak axial asymmetry

The question of preservation of the third adiabatic invariant motion of charged particles $v_{II} = 0$ (equatorial plane) in the flow and the canonical form in magnetic fields having a weak asymmetry. Go to rotating with the angular velocity of the drift coordinate system allows us to reduce the problem to have been solved, namely, the task of saving the third adiabatic invariant in the axially symmetric, but the time-varying magnetic field.