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A Lie Deprit perturbation algorithm for linear differential equations with periodic coefficients

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Figure 1. Top: one of the characteristic exponents of system (50), obtained by direct numerical integration (solid line), and by the  pertur-bative algorithm of order ε 10 (dot-dashed line), ε 15 (dashed line) and ε 22 (dotted line), as a function of ε
Figure 2. Different approximations for the first characteristic curve of the Mathieu equation ¨ x + (a + ε cos 2t)x = 0 in the space of parameters (a, ε)

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