Geodesic
Criterion of Lyapunov reducibility of a linear autonomous differential system to a linear autonomous equation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 55-59 
I. N. Sergeev; K. V. Umansky. Criterion of Lyapunov reducibility of a linear autonomous differential system to a linear autonomous equation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 55-59. http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish a unified criterion for the reducibility of a linear homogeneous differential system with constant coefficients to a linear homogeneous differential equation with constant coefficients by means of both Lyapunov and periodic transformations. The resulting necessary and sufficient condition on a system is formulated in terms of properties of the Jordan normal form of its matrix.

[1] Lyapunov A.M., Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhizdat, M.–L., 1950

[2] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967

[3] Zaitsev B.A., “Globalnaya dostizhimost i globalnaya lyapunovskaya privodimost dvumernykh i trekhmernykh lineinykh upravlyaemykh sistem s postoyannymi koeffitsientami”, Vestn. Udmurt. un-ta. Matem., 2003, no. 1, 31–62

[4] Sergeev I.N., “Ob upravlenii resheniyami lineinogo differentsialnogo uravneniya”, Vestn. Mosk. un-ta. Matem. Mekhan., 2009, no. 3, 25–33

[5] Sergeev I.N., “O privodimosti lineinykh differentsialnykh sistem k lineinym differentsialnym uravneniyam”, Vestn. Mosk. un-ta. Matem. Mekhan., 2019, no. 3, 39–44

[6] Demidovich B.P., “Ob odnom obobschenii kriteriya ustoichivosti Lyapunova dlya pravilnykh sistem”, Matem. sb., 66(108):3 (1965), 344–353