Geodesic
Exponential Dichotomy of Linear Systems of Differential Equations with Periodic Coefficients
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 40-48 
G. V. Demidenko; Yu. Yu. Klevtsova. Exponential Dichotomy of Linear Systems of Differential Equations with Periodic Coefficients. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 40-48. http://geodesic.mathdoc.fr/item/VNGU_2008_8_4_a4/
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     title = {Exponential {Dichotomy} of {Linear} {Systems} of {Differential} {Equations} with {Periodic} {Coefficients}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions of exponential dichotomy of linear systems of differential equations with periodic coefficients are established. The results are stated in terms of solvability of a special boundary value problem for the Lyapunov differential equations. Estimates of dichotomy parameters and multipliers of the systems are given.

[1] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970

[2] Massera Kh., Sheffer Kh., Lineinye differentsialnye uravneniya i funktsionalnye prostranstva, Mir, M., 1970

[3] Rozenvasser E. N., Pokazateli Lyapunova v teorii lineinykh sistem upravleniya, Nauka, M., 1977

[4] Maizel A. D., “Ob ustoichivosti reshenii sistem differentsialnykh uravnenii”, Tr. Uralskogo politekhnicheskogo in-ta, ser. matem., 51 (1954), 20–50

[5] Samoilenko A. M., Kulik V. L., “Eksponentsialnaya dikhotomiya invariantnogo tora dinamicheskikh sistem”, Differents. uravn., 15:8 (1979), 1434–1443

[6] Demidenko G. V., Matveeva I. I., “Ob ustoichivosti reshenii lineinykh sistem s periodicheskimi koeffitsientami”, Sib. mat. zhurn., 42:2 (2001), 332–348

[7] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauchnaya kniga, Novosibirsk, 1997

[8] Bulgak A., Bulgak H., Linear Algebra, Selcuk University, Konya, 2001