Adiabatic Invariants of Periodic Classical Systems

Recently there has been renewed interest in adiabatic invariants of simply-periodic classical systems subject to perturbation by slow variation of parameters. In several interesting cases it has been shown that if the system varies slowly from one steady state to a different steady state, the appropriate adiabatic invariant is constant to an arbitrarily high order in a slowness parameter.It is shown here how these and similar results may be derived by systematic use of a technique of perturbation theory of classical Hamiltonian systems. The method is essentially iteration of the transformation to action and angle variables.