Geodesic
Analysis of nonautonomous systems of ordinary differential equations with exponentially periodic matrix
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 62-69

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We investigate a class of nonautonomous systems of ordinary differential equations whose matrix can be characterized as exponentially periodic. We develop the algorithm of spectral analysis of these systems. By this algorithm we prove reducibility theorems. The proposed algorithm is based on the splitting method that allows to reduce considered systems to simpler systems with quasi-diagonal matrix and formulate constructive conditions of solutions stability.
Keywords: nonautonomous systems of ordinary differential equations, exponentially periodic matrix, quasi-reducibility, splitting method, stability. 
@article{IVM_2017_10_a6,
     author = {Yu. A. Konyaev and D. A. Maslov},
     title = {Analysis of nonautonomous systems of ordinary differential equations with exponentially periodic matrix},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--69},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_10_a6/}
}
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Yu. A. Konyaev; D. A. Maslov. Analysis of nonautonomous systems of ordinary differential equations with exponentially periodic matrix. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 62-69. http://geodesic.mathdoc.fr/item/IVM_2017_10_a6/