Abstract
Linear and quadratic gyrokinetic current response operators are derived in a form which exhibits a formal symmetry of basic importance. The symmetry is the mathematical origin of the approximative conservation of wave action. The gyrophase has been eliminated by means of an averaging transformation using a recently developed noncanonical Hamiltonian pertubation method. Previous intergrations along unperturbed orbits are changed to integrals along uperterbed guiding center orbits. There are no restrictions (like low frequency) on the pertubation. Inserting the current response operators in Maxwell's equations yields a selfconsistent nonlinear gyrokinetic wave equation for the electromagnetic 4-potential in an inhomogeneous Vlasov-plasma.
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