Geodesic
Asymptotic analogs of the Floquet--Lyapunov theorem for some classes of periodic systems of ordinary differential equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 46-54

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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.
Keywords: system of ordinary differential equations, Cauchy problem, singularly perturbed system, splitting method, small parameter. 
@article{IVM_2010_4_a4,
     author = {E. Yu. Romanova},
     title = {Asymptotic analogs of the {Floquet--Lyapunov} theorem for some classes of periodic systems of ordinary differential equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--54},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_4_a4/}
}
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E. Yu. Romanova. Asymptotic analogs of the Floquet--Lyapunov theorem for some classes of periodic systems of ordinary differential equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 46-54. http://geodesic.mathdoc.fr/item/IVM_2010_4_a4/