Geodesic
Systems of linear differential equations with non-$x$-autonomous basic Lie algebra
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 112-123

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We obtain some necessary and sufficient conditions for the non-$x$-autonomy of the basic Lie algebra of a system of first-order linear differential equations with constant coefficients over the field of complex numbers. Using these results, we establish the $x$-autonomy of the basic Lie algebra of some systems of equations of mathematical physics.
Keywords: $x$-autonomy of the basic Lie algebra, canonical systems of linear differential equations, criteria of $x$-autonomy. 
@article{SJIM_2011_14_2_a13,
     author = {Yu. A. Chirkunov},
     title = {Systems of linear differential equations with non-$x$-autonomous basic {Lie} algebra},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {112--123},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a13/}
}
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Yu. A. Chirkunov. Systems of linear differential equations with non-$x$-autonomous basic Lie algebra. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 112-123. http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a13/