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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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).

[1] Lyapunov A.M., Sobr. soch., v 6 t., v. 2, Izd-vo AN SSSR, M.; L., 1956

[2] Bylov B.F., Vinograd R.E., Grobman D.M., Nemytskii V.V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR | Zbl

[3] Perron O., “Über lineare Differentialgleichungen, bei denen die unabhängige Variable reel ist”, J. reine und angew. Math., 142:4 (1913), 254–270 ; 143:1, 25–50 | DOI | MR | Zbl

[4] Millionschikov V.M., “Grubye svoistva lineinykh sistem differentsialnykh uravnenii”, Differents. uravneniya, 5:10 (1969), 1775–1784

[5] Bylov B.F., Izobov N.A., “Neobkhodimye i dostatochnye usloviya ustoichivosti kharakteristicheskikh pokazatelei lineinoi sistemy”, Differents. uravneniya, 5:10 (1969), 1794–1803 | MR | Zbl

[6] Nurmatov A.M., Neobkhodimye usloviya ustoichivosti kharakteristicheskikh pokazatelei Lyapunova lineinykh differentsialnykh sistem pri eksponentsialno ubyvayuschikh vozmuscheniyakh, Dep. v VINITI 12.03.1987. No 1811–B87, Differents. uravneniya, Minsk, 1987 | Zbl

[7] Nurmatov A.M., “Neobkhodimye usloviya ustoichivosti kharakteristicheskikh pokazatelei Lyapunova lineinykh differentsialnykh sistem pri eksponentsialno ubyvayuschikh vozmuscheniyakh”, Differents. uravneniya, 25:2 (1989), 335–336 | Zbl

[8] Barabanov E.A., Denisenko N.S., “Neobkhodimoe i dostatochnoe uslovie ustoichivosti pokazatelei Lyapunova lineinykh differentsialnykh sistem pri eksponentsialno ubyvayuschikh vozmuscheniyakh”, Differents. uravneniya, 43:2 (2007), 165–175 | MR | Zbl

[9] Sergeev I.N., “Tochnye verkhnie granitsy podvizhnosti pokazatelei Lyapunova sistemy differentsialnykh uravnenii i povedenie pokazatelei pri vozmuscheniyakh, stremyaschikhsya k nulyu na beskonechnosti”, Differents. uravneniya, 16:3 (1980), 438–448 | MR | Zbl

[10] Barabanov E.A., Tochnye granitsy krainikh pokazatelei Lyapunova lineinykh differentsialnykh sistem pri eksponentsialnykh i stepennykh vozmuscheniyakh, Avtoref. dis. ... kand. fiz.-mat. nauk, Minsk, 1984

[11] Bylov B.F., Izobov N.A., “Neobkhodimye i dostatochnye usloviya ustoichivosti kharakteristicheskikh pokazatelei diagonalnoi sistemy”, Differents. uravneniya, 5:10 (1969), 1785–1793 | MR | Zbl

[12] Bylov B.F., “Obobschenie teoremy Perrona”, Differents. uravneniya, 1:12 (1965), 1597–1600 | MR | Zbl

[13] Millionschikov V.M., “Dokazatelstvo dostizhimosti tsentralnykh pokazatelei”, Sib. mat. zhurn., 10:1 (1969), 99–104

[14] Izobov N.A., “Lineinye sistemy obyknovennykh differentsialnykh uravnenii”, Itogi nauki i tekhniki. Mat. analiz, 12, VINITI, M., 1974, 71–146 | MR

[15] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[16] Bylov B.F., “O privedenii lineinoi sistemy k blochno-treugolnomu vidu”, Differents. uravneniya, 23:12 (1987), 2027–2031 | MR