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A technique based on the Campbell-Baker-Hausdorff (CBH) formula is introduced to calculate the effective Hamiltonian for kicked dynamics, classical and quantum. An integrable example is exactly solved by this method. A non-integrable kicked spin dynamics is treated approximately up to seventh order in a perturbation parameter. The CBH expansion is evaluated in a transparent way with the help of a REDUCE program, thereby illustrating that the CBH expansion is asymptotic.
Rainer Scharf (Sat,) studied this question.