Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 93-98
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E. V. Musafirov. On simple linear differential systems with an even matrix. Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 93-98. http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a8/
@article{TIMB_2010_18_2_a8,
author = {E. V. Musafirov},
title = {On simple linear differential systems with an even matrix},
journal = {Trudy Instituta matematiki},
pages = {93--98},
year = {2010},
volume = {18},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a8/}
}
TY - JOUR
AU - E. V. Musafirov
TI - On simple linear differential systems with an even matrix
JO - Trudy Instituta matematiki
PY - 2010
SP - 93
EP - 98
VL - 18
IS - 2
UR - http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a8/
LA - ru
ID - TIMB_2010_18_2_a8
ER -
%0 Journal Article
%A E. V. Musafirov
%T On simple linear differential systems with an even matrix
%J Trudy Instituta matematiki
%D 2010
%P 93-98
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a8/
%G ru
%F TIMB_2010_18_2_a8
Conditions of simplicity of linear differential systems with an even coefficient matrix are obtained. Fundamental matrixes of solutions of linear differential systems $\dot{x}=2P(t)x$ and $\dot{x}=-2P(-t)x$ are expressed by means of reflective matrix $F(t)$ of simple system $\dot{x}=P(t)x$, $t\in\mathbb{R}$, $x\in\mathbb{R}^n$. Fundamental matrixes of solutions of systems $\dot{x}=-2kP(t)x$, $k\in\mathbb{Z}$ and $\dot{x}=-2P(t)x+\dot{P}(t)P^{-1}(t)x$ are also expressed by means of $F(t)$ under condition of evenness of matrix $P(t)$. Equivalence (in terms of coincidence of reflective functions) of last system and a simple system $\dot{x}=-2P(t)x$ with an even coefficient matrix is proved.
