Asymptotic analogs of the Floquet–Lyapunov theorem for some classes of periodic systems of ordinary differential equations

We prove asymptotic analogs of the Floquet–Lyapunov theorem and some reducibility theorems for various classes of linear and quasilinear systems of ordinary differential equations with periodic matrices with large and small amplitudes. We study such problems with the help of new versions of the splitting method in the theory of regular and singular perturbations, which complements the known results. We also adduce several examples.