Abstract
A perturbative procedure based on the Lie--Deprit algorithm of classical mechanics is proposed to compute analyticapproximations to the fundamental matrix of linear differential equations with periodic coefficients.These approximations reproduce the structure assured by the Floquet theorem. Alternatively,the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodicproblem to an autonomous system and also to its characteristic exponents. The procedure is computationally well adapted and converges for sufficiently small values of the perturbationparameter. Moreover, when the system evolves in a Lie group, the approximationsalso belong to the same Lie group, thus preserving qualitative properties of the exact solution.
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