Geodesic
Reducibility of linear differential systems to linear differential equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2019), pp. 39-44 
I. N. Sergeev. Reducibility of linear differential systems to linear differential equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2019), pp. 39-44. http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a4/
@article{VMUMM_2019_3_a4,
     author = {I. N. Sergeev},
     title = {Reducibility of linear differential systems to linear differential equations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {39--44},
     year = {2019},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a4/}
}
TY  - JOUR
AU  - I. N. Sergeev
TI  - Reducibility of linear differential systems to linear differential equations
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 39
EP  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a4/
LA  - ru
ID  - VMUMM_2019_3_a4
ER  - 
%0 Journal Article
%A I. N. Sergeev
%T Reducibility of linear differential systems to linear differential equations
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 39-44
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a4/
%G ru
%F VMUMM_2019_3_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is established. The preservation of the additional property of periodicity of coefficients is guaranteed, and for two-dimensional or complex systems the constancy of their coefficients is preserved. The differences in feasibility of asymptotic and generalized Lyapunov reducibility from Lyapunov one are indicated.

[1] Zaitsev V. A., “Globalnaya dostizhimost i globalnaya lyapunovskaya privodimost dvumernykh i trekhmernykh lineinykh upravlyaemykh sistem s postoyannymi koeffitsientami”, Vestn. Udmurt. un-ta. Matem., 1 (2003), 31–62

[2] Sergeev I. N., “O predelnykh znacheniyakh lyapunovskikh pokazatelei lineinykh uravnenii”, Differents. uravneniya, 46:11 (2010), 1664–1665

[3] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

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

[5] Sergeev I. N., “O pokazatelyakh koleblemosti, vraschaemosti i bluzhdaemosti differentsialnykh sistem, zadayuschikh povoroty ploskosti”, Vestn. Mosk. un-ta. Matem. Mekhan., 2019, no. 1, 21–26

[6] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR

[7] Basov V. P., “O strukture reshenii pravilnoi differentsialnoi sistemy”, Vestn. Leningr. un-ta, 1952, no. 12, 3–8

[8] Bogdanov Yu. S., “K teorii sistem lineinykh differentsialnykh uravnenii”, Dokl. AN SSSR, 104:6 (1955), 813–814 | Zbl

[9] Grobman D. M., “Kharakteristicheskie pokazateli sistem, blizkikh k lineinym”, Matem. sb., 30(72):1 (1952), 121–166 | MR | Zbl