Guiding-center Recursive Vlasov method and Lie-transforms in plasma physics

The gyrocenter phase-space transformation is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The purpose of the present work is to clarify the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center Recursive Vlasov method and the method of Lie-transform phase-space transformations. A discussion of a recent application [1] of the Recursive Vlasov method is included. [1] F.I. Parra and P.J. Catto, Plasma Phys. Control. Fusion \textbf{50}, 065014 (2008)