Geodesic
The estimate of accuracy of the rational approximation of the monodromy operator
Eurasian mathematical journal, Tome 9 (2018) no. 1, pp. 88-91.

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

The paper deals with the problem of investigation of eigenvalues of the monodromy operator for periodic solutions of nonlinear delay-differential equations. In the case the period of the solution is not commensurate with the delay time, the rational approximation is used. Thus the eigenvalues depend on the perturbation parameter. In this paper, a similar problem for a nonlinear system of ordinary differential equations is considered. Necessary and sufficient conditions for the Lipschitz behaviour of the eigenvalues are obtained. 
@article{EMJ_2018_9_1_a6,
     author = {N. B. Zhuravlev and A. N. Sokolova},
     title = {The estimate of accuracy of the rational approximation of the monodromy operator},
     journal = {Eurasian mathematical journal},
     pages = {88--91},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a6/}
}
TY  - JOUR
AU  - N. B. Zhuravlev
AU  - A. N. Sokolova
TI  - The estimate of accuracy of the rational approximation of the monodromy operator
JO  - Eurasian mathematical journal
PY  - 2018
SP  - 88
EP  - 91
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a6/
LA  - en
ID  - EMJ_2018_9_1_a6
ER  - 
%0 Journal Article
%A N. B. Zhuravlev
%A A. N. Sokolova
%T The estimate of accuracy of the rational approximation of the monodromy operator
%J Eurasian mathematical journal
%D 2018
%P 88-91
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a6/
%G en
%F EMJ_2018_9_1_a6
N. B. Zhuravlev; A. N. Sokolova. The estimate of accuracy of the rational approximation of the monodromy operator. Eurasian mathematical journal, Tome 9 (2018) no. 1, pp. 88-91. http://geodesic.mathdoc.fr/item/EMJ_2018_9_1_a6/

[1] B.P. Demidovich, Lectures on mathematical theory of stability, Nauka, M., 1967 | MR

[2] J.K. Hale, Theory of functional differential equations, Springer, New York, 1977 | MR

[3] F. Hartman, Ordinary differential equations, Wiley, New York, 1964 | MR

[4] A.L. Skubachevskii, H.-O. Walther, “On the Floquet multipliers of periodic solutions to nonlinear functional differential equations”, J. Dynam. Differential Equations, 18:2 (2006), 257–355 | DOI | MR

[5] M.M. Vainberg, V.A. Trenogin, Theory of the branching of solutions of nonlinear equations, Nauka, M., 1969 | MR

[6] M.I. Vishik, L.A. Lusternik, “The solution of some perturbation problems for matrices and selfadjoint or non-selfadjoint differential equations I”, Russian Mathematical Surveys, 15:3 (1960), 1–73 | DOI | MR

[7] N.B. Zhuravlev, “Hyperbolicity criterion for periodic solutions of functional-differential equations with several delays”, Journal of Mathematical Sciences, 153:5 (2008), 683–709 | DOI | MR

[8] N.B. Zhuravlev, “An approximate calculation of the Floquet multipliers for periodic solutions of delay-differential equations”, Proceedings of the 21th Crimean Autumn Mathematical School-Symposium, Spectral and evolution problems, 22, Simferopol, 2012, 76–80