Geodesic
Linear differential Lappo-Danilevskii systems
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 275-282

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MR Zbl
The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.
The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.
DOI : 10.21136/MB.2002.134159
Classification : 34A30, 34C41
Keywords: linear differential systems; Lyapunov transformations; functional commutative matrices; Lappo-Danilevskii systems 
Mazanik, S. A. Linear differential Lappo-Danilevskii systems. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 275-282. doi: 10.21136/MB.2002.134159
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[1] B. P. Demidovich: Lectures on the Mathematical Stability Theory. Nauka, Moskva, 1967. (Russian) | MR

[2] T. L. Surin: On Lyapunov exponents of regular Lappo-Danilevskii systems. Differ. Uravn. 25 (1989), 543–545. (Russian) | MR

[3] B. F. Bylov, R. E. Vinograd, D. M. Grobman, V. V. Nemytskii: Theory of Lyapunov Exponents and Its Applications to Stability Problems. Nauka, Moskva, 1966. (Russian)

[4] Yu. S. Bogdanov: Asymptotically equivalent linear differential systems. Differ. Equations 1 (1965), 541–549. | MR | Zbl

[5] V. A. Vinokurov: Explicit solution of a linear ordinary differential equation and the main property of the exponential function. Differ. Equations 33 (1997), 298–304. | MR

[6] L. A. Mazanik, S. A. Mazanik: On irreducibility of linear differential systems to systems with functional commutative matrices of coefficients. Vestn. Beloruss. Gos. Univ. Ser.  1. Fiz. Mat. Inform. (1997), no. 3, 42–46. (Russian) | MR

[7] S. A. Mazanik: On irreducibility of linear differential systems to Lappo-Danilevskii systems. Dokl. Akad. Nauk Belarusi 41 (1997), no. 6, 30–33. (Russian) | MR

[8] N. A. Izobov: Linear systems of ordinary differential equations. Itogi Nauki i Tekhniki, Mat. Analiz. 12 (1974), 71–146. (Russian) | MR

[9] S. A. Mazanik: Irreducibility of linear systems by generalized Lyapunov transformations to systems with functionally commutative coefficient matrices. Differ. Equations 34 (1998), 755–761. | MR | Zbl

[10] S. A. Mazanik: On the impossibility to reduce linear systems by a generalized Lyapunov transformation to Lappo-Danilevskii systems. Differ. Equations 34 (1998), 1082–1085. | MR | Zbl

[11] S. A. Mazanik: Lappo-Danilevskii systems in the set of linear systems. Differ. Equations 35 (1999), 90–96. | MR | Zbl

[12] J. F. P. Martin: On the exponential representation of solutions of linear differential equations. J. Differ. Equations (1968), 257–279. | MR | Zbl

[13] V. N. Laptinskii: Linear differential systems. Differ. Equations 38 (1972), 188–191. | Zbl

[14] S. A. Mazanik: Exponential representation of solutions of linear matrix differential equation. Differ. Equations 27 (1991), 130–135. | MR

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