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In this paper, we show how to use canonical perturbation theory fordissipative dynamical systems capable of showing limit cycle oscillations.Thus, our work surmounts the hitherto perceived barrier for canonicalperturbation theory that it can be applied only to a class of conservativesystems, viz.,~Hamiltonian systems. In the process, we also find Hamiltonianstructure for an important subset of Li\'enard system--- a paradigmatic systemfor modeling isolated and asymptotic oscillatory state. We discuss thepossibility of extending our method to encompass even wider range ofnon-conservative systems.

Conservative perturbation theory for nonconservative systems