Geodesic
The necessary condition of Lyapunov exponents stability of linear differential systems under degree decreasing perturbations
Trudy Instituta matematiki, Tome 16 (2008) no. 2, pp. 105-117

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The necessary condition, that must be satisfied by a linear differential system, is received, so that its Lyapunov exponents spectrum does not change under all degree decreasing perturbations of its matrix of coefficients, which decrease at infinity not slower that a degree function does (which is own for each perturbation). 
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     author = {N. S. Niparko},
     title = {The necessary condition of {Lyapunov} exponents stability of linear differential systems under degree decreasing perturbations},
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N. S. Niparko. The necessary condition of Lyapunov exponents stability of linear differential systems under degree decreasing perturbations. Trudy Instituta matematiki, Tome 16 (2008) no. 2, pp. 105-117. http://geodesic.mathdoc.fr/item/TIMB_2008_16_2_a10/