A criterion for a small change in the direction of the solutions of a linear system of differential equations as the result of small disturbances in the coefficients of the system
Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 173-180
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It is shown that of the systems $\dot x=A(t)x$, only systems with integral separability have the following property: when $\sup\limits_t\|B(t)-A(t)\|$ is small, to each solution $y(t)$ of the system $\dot y=B(t)y$, one may associatea solution $x(t)$ of the system $\dot x=A(t)x$, such that the angle between the vectors $x(t)$, $y(t)$ is small for all $t$.
@article{MZM_1968_4_2_a8,
author = {V. M. Millionshchikov},
title = {A~criterion for a small change in the direction of the solutions of a~linear system of differential equations as the result of small disturbances in the coefficients of the system},
journal = {Matemati\v{c}eskie zametki},
pages = {173--180},
year = {1968},
volume = {4},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a8/}
}
TY - JOUR AU - V. M. Millionshchikov TI - A criterion for a small change in the direction of the solutions of a linear system of differential equations as the result of small disturbances in the coefficients of the system JO - Matematičeskie zametki PY - 1968 SP - 173 EP - 180 VL - 4 IS - 2 UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a8/ LA - ru ID - MZM_1968_4_2_a8 ER -
%0 Journal Article %A V. M. Millionshchikov %T A criterion for a small change in the direction of the solutions of a linear system of differential equations as the result of small disturbances in the coefficients of the system %J Matematičeskie zametki %D 1968 %P 173-180 %V 4 %N 2 %U http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a8/ %G ru %F MZM_1968_4_2_a8
V. M. Millionshchikov. A criterion for a small change in the direction of the solutions of a linear system of differential equations as the result of small disturbances in the coefficients of the system. Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 173-180. http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a8/