Geodesic
On simple linear differential systems with an even matrix
Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 93-98.

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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. 
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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/

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