Geodesic
Methods for studying the stability of linear periodic systems depending on a small parameter
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations, Tome 163 (2019), pp. 113-126

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In this paper, we consider systems of linear differential equations with periodic coefficients depending on a small parameter. We propose new approaches to the problem of constructing a monodromy matrix that lead to new effective formulas for calculating multipliers of the system studies. We present a number of applications in problems of the perturbation theory of linear operators, in the analysis of stability of linear differential equations with periodic coefficients, in the problem of constructing the stability domains of linear dynamical systems, etc.
Keywords: differential equation, periodic system, Hamiltonian system, stability, small parameter.
Mots-clés : monodromy matrix, multiplier 
@article{INTO_2019_163_a8,
     author = {M. G. Yumagulov and L. S. Ibragimova and A. S. Belova},
     title = {Methods for studying the stability of linear periodic systems depending on a small parameter},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {113--126},
     publisher = {mathdoc},
     volume = {163},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_163_a8/}
}
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M. G. Yumagulov; L. S. Ibragimova; A. S. Belova. Methods for studying the stability of linear periodic systems depending on a small parameter. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations, Tome 163 (2019), pp. 113-126. http://geodesic.mathdoc.fr/item/INTO_2019_163_a8/