Linear differential Lappo-Danilevskii systems

S. A. Mazanik

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 275-282
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Mazanik, S. A.. "Linear differential Lappo-Danilevskii systems." Mathematica Bohemica 127.2 (2002): 275-282. <http://eudml.org/doc/249055>.

@article{Mazanik2002,
abstract = {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.},
author = {Mazanik, S. A.},
journal = {Mathematica Bohemica},
keywords = {linear differential systems; Lyapunov transformations; functional commutative matrices; Lappo-Danilevskii systems; linear differential systems; Lyapunov transformations; functional commutative matrices; Lappo-Danilevskii systems},
language = {eng},
number = {2},
pages = {275-282},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear differential Lappo-Danilevskii systems},
url = {http://eudml.org/doc/249055},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Mazanik, S. A.
TI - Linear differential Lappo-Danilevskii systems
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 275
EP - 282
AB - 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.
LA - eng
KW - linear differential systems; Lyapunov transformations; functional commutative matrices; Lappo-Danilevskii systems; linear differential systems; Lyapunov transformations; functional commutative matrices; Lappo-Danilevskii systems
UR - http://eudml.org/doc/249055
ER -

References

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  1. Lectures on the Mathematical Stability Theory, Nauka, Moskva, 1967. (Russian) (1967) MR0226126
  2. On Lyapunov exponents of regular Lappo-Danilevskii systems, Differ. Uravn. 25 (1989), 543–545. (Russian) (1989) MR0994342
  3. Theory of Lyapunov Exponents and Its Applications to Stability Problems, Nauka, Moskva, 1966. (Russian) (1966) 
  4. Asymptotically equivalent linear differential systems, Differ. Equations 1 (1965), 541–549. (1965) Zbl0155.41002MR0199481
  5. Explicit solution of a linear ordinary differential equation and the main property of the exponential function, Differ. Equations 33 (1997), 298–304. (1997) MR1615397
  6. 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) (1997) MR1672690
  7. On irreducibility of linear differential systems to Lappo-Danilevskii systems, Dokl. Akad. Nauk Belarusi 41 (1997), no. 6, 30–33. (Russian) (1997) MR1668963
  8. Linear systems of ordinary differential equations, Itogi Nauki i Tekhniki, Mat. Analiz. 12 (1974), 71–146. (Russian) (1974) MR0402152
  9. Irreducibility of linear systems by generalized Lyapunov transformations to systems with functionally commutative coefficient matrices, Differ. Equations 34 (1998), 755–761. (1998) Zbl1075.34503MR1690879
  10. On the impossibility to reduce linear systems by a generalized Lyapunov transformation to Lappo-Danilevskii systems, Differ. Equations 34 (1998), 1082–1085. (1998) Zbl1122.34301MR1699479
  11. Lappo-Danilevskii systems in the set of linear systems, Differ. Equations 35 (1999), 90–96. (1999) Zbl0938.34004MR1723208
  12. On the exponential representation of solutions of linear differential equations, J. Differ. Equations (1968), 257–279. (1968) Zbl0174.39204MR0223631
  13. Linear differential systems, Differ. Equations 38 (1972), 188–191. (1972) Zbl0279.34006
  14. Exponential representation of solutions of linear matrix differential equation, Differ. Equations 27 (1991), 130–135. (1991) MR1109379

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