Geodesic
On a generic property of vector subspaces defined by Lyapunov exponents
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 1-18 
V. M. Millionshchikov. On a generic property of vector subspaces defined by Lyapunov exponents. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the dependence on a Cauchy problem of the subspace consisting of the initial values of those solutions of the linearized Cauchy problem whose Lyapunov exponents do not exceed the $k$th Lyapunov exponent of the linearized system is generically continuous, provided that the $k$th exponent of the linearized system is different from its $(k-1)$st exponent. Bibliography: 11 titles.

[1] Lyapunov A. M., Sobr. soch., t. 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] Izobov N. A., “Lineinye sistemy obyknovennykh differentsialnykh uravnenii”, Itogi nauki i tekhniki. Matem. analiz, 12, VINITI, M., 1974, 71–146 | MR

[4] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. X”, Differents. uravneniya, 18 (1982), 2132–2148 | Zbl

[5] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. IV”, Differents. uravneniya, 17 (1981), 431–468

[6] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. XI”, Differents. uravneniya, 19 (1983), 196–214 | Zbl

[7] Millionschikov V. M., “Ob indeksakh eksponentsialnoi razdelennosti”, Matem. sb., 124(166) (1984), 451–485 | MR | Zbl

[8] Millionschikov V. M., “O tipichnom povedenii uslovnoi eksponentsialnoi ustoichivosti pri vozmuscheniyakh”, Matem. sb., 125(167) (1984), 435–457

[9] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. V”, Differents. uravneniya, 17 (1981), 1394–1410

[10] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. VIII”, Differents. uravneniya, 18 (1982), 1330–1345

[11] Millionschikov V. M., “Berovskie klassy funktsii i pokazateli Lyapunova. IX”, Differents. uravneniya, 18 (1982), 1507–1548