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

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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. 
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     title = {Criterion of {Lyapunov} reducibility of a linear autonomous differential system to a linear autonomous equation},
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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/