| Title:
|
Linear differential Lappo-Danilevskii systems (English) |
| Author:
|
Mazanik, S. A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
275-282 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear differential systems |
| Keyword:
|
Lyapunov transformations |
| Keyword:
|
functional commutative matrices |
| Keyword:
|
Lappo-Danilevskii systems |
| MSC:
|
34A30 |
| MSC:
|
34C41 |
| idZBL:
|
Zbl 1016.34047 |
| idMR:
|
MR1981532 |
| DOI:
|
10.21136/MB.2002.134159 |
| . |
| Date available:
|
2012-10-05T13:01:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134159 |
| . |
| Reference:
|
[1] B. P. Demidovich: Lectures on the Mathematical Stability Theory.Nauka, Moskva, 1967. (Russian) MR 0226126 |
| Reference:
|
[2] T. L. Surin: On Lyapunov exponents of regular Lappo-Danilevskii systems.Differ. Uravn. 25 (1989), 543–545. (Russian) MR 0994342 |
| Reference:
|
[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) |
| Reference:
|
[4] Yu. S. Bogdanov: Asymptotically equivalent linear differential systems.Differ. Equations 1 (1965), 541–549. Zbl 0155.41002, MR 0199481 |
| Reference:
|
[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 1615397 |
| Reference:
|
[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 1672690 |
| Reference:
|
[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 1668963 |
| Reference:
|
[8] N. A. Izobov: Linear systems of ordinary differential equations.Itogi Nauki i Tekhniki, Mat. Analiz. 12 (1974), 71–146. (Russian) MR 0402152 |
| Reference:
|
[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. Zbl 1075.34503, MR 1690879 |
| Reference:
|
[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. Zbl 1122.34301, MR 1699479 |
| Reference:
|
[11] S. A. Mazanik: Lappo-Danilevskii systems in the set of linear systems.Differ. Equations 35 (1999), 90–96. Zbl 0938.34004, MR 1723208 |
| Reference:
|
[12] J. F. P. Martin: On the exponential representation of solutions of linear differential equations.J. Differ. Equations (1968), 257–279. Zbl 0174.39204, MR 0223631 |
| Reference:
|
[13] V. N. Laptinskii: Linear differential systems.Differ. Equations 38 (1972), 188–191. Zbl 0279.34006 |
| Reference:
|
[14] S. A. Mazanik: Exponential representation of solutions of linear matrix differential equation.Differ. Equations 27 (1991), 130–135. MR 1109379 |
| . |
