Exponential dichotomy for systems of difference equations under perturbation of coefficients
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 4, pp. 561-572.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of exponential dichotomy for systems of difference equations with periodic coefficients is considered. Based on the previously obtained exponential dichotomy criterion, the question of permissible perturbations on the coefficient matrix, under which the exponential dichotomy persists, is investigated.
Keywords: system of difference equations with periodic coefficients, system of discrete Lyapunov equations, exponential dichotomy criterion, perturbation of coefficients.
@article{CHFMJ_2024_9_4_a2,
     author = {G. V. Demidenko and A. A. Bondar' and M. Sh. Ganzhaeva},
     title = {Exponential dichotomy for systems of difference equations under perturbation of coefficients},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {561--572},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a2/}
}
TY  - JOUR
AU  - G. V. Demidenko
AU  - A. A. Bondar'
AU  - M. Sh. Ganzhaeva
TI  - Exponential dichotomy for systems of difference equations under perturbation of coefficients
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2024
SP  - 561
EP  - 572
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a2/
LA  - ru
ID  - CHFMJ_2024_9_4_a2
ER  - 
%0 Journal Article
%A G. V. Demidenko
%A A. A. Bondar'
%A M. Sh. Ganzhaeva
%T Exponential dichotomy for systems of difference equations under perturbation of coefficients
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2024
%P 561-572
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a2/
%G ru
%F CHFMJ_2024_9_4_a2
G. V. Demidenko; A. A. Bondar'; M. Sh. Ganzhaeva. Exponential dichotomy for systems of difference equations under perturbation of coefficients. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 4, pp. 561-572. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a2/

[1] Daleckii Yu.L., Krein M.G., Stability of Solutions to Differential Equations in Banach Space, American Mathematical Society, Providence, 1974

[2] Godunov S.K., Modern Aspects of Linear Algebra, American Mathematical Society, Providence, 1998

[3] Bulgak A., Bulgak H., Linear algebra, Selcuk University, Konya, 2001

[4] Abramov A.A., “On the boundary conditions at a singular point for linear ordinary differential equations”, USSR Computational Mathematics and Mathematical Physics, 11:1 (1971), 363–367

[5] Roberts J. D., “Linear model reduction and solution of the algebraic Riccati equation by use of the sign function”, International Journal of Control, 32:4 (1980), 677–687

[6] Balzer L. A., “Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other matrix equations”, International Journal of Control, 32:6 (1980), 1057–1078

[7] Bulgakov A.Ya., Godunov S.K., “Circular dichotomy of the spectrum of a matrix”, Siberian Mathematical Journal, 29:5 (1988), 734–744

[8] Bulgak H., “Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability”, Error Control and Adaptivity in Scientific Computing, eds. H. Bulgak, C. Zenger, Springer, Dordrecht, 1999, 95–124

[9] Bondar A.A., “On conditions for exponential dichotomy for systems of difference equations under perturbation of coefficients”, Mathematical Notes of NEFU, 26:4 (2019), 3–13

[10] Aydin K., Bulgak H., Demidenko G.V., “Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients”, Siberian Mathematical Journal, 43:3 (2002), 389–401

[11] Demidenko G.V., Matrix Equations, Textbook, Novosibirsk State University, Novosibirsk, 2009 (In Russ.)

[12] Demidenko G.V., Bondar A.A., “Exponential dichotomy of systems of linear difference equations with periodic coefficients”, Siberian Mathematical Journal, 57:6 (2016), 969–980

[13] Demidenko G. V., “Stability of solutions to difference equations with periodic coefficients in linear terms”, Journal of Computational Mathematics and Optimization, 6:1 (2010), 1–12

[14] Demidenko G.V., “Systems of differential equations with periodic coefficients”, Journal of Applied and Industrial Mathematics, 8:1 (2014), 20–27

[15] Demidenko G.V., “On one class of systems of differential equations with periodic coefficients in linear terms”, Siberian Mathematical Journal, 62:5 (2021), 805–821