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The conjugate variable method, an essential ingredient in the path-integral formalism of classical statistical dynamics, is used to apply the Hamilton-Lie perturbation theory to a system of ordinary differential equations that does not have the Hamiltonian dynamic structure. The method endows the system with this structure by doubling the unknown variables; hence, the canonical Hamilton-Lie perturbation theory becomes applicable to the system. The method is applied to two classical problems of plasma physics to demonstrate its effectiveness and study its properties: a non-linear oscillator that can explode and the guiding center motion of a charged particle in a magnetic field.

The Conjugate Variable Method in Hamilton-Lie Perturbation Theory - Applications to Plasma Physics -