Geodesic
On branching of periodic solutions of quasilinear systems of ordinary differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 3-10

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In this paper, a normal system of ordinary differential equations with a small parameter is examined. We obtain conditions for the existence and stability of a periodic solution, which, at the zero value of the parameter, satisfies a linear homogeneous system. The reasoning is based on the analysis of properties of the monodromy operator.
Keywords: differential equation, periodic solution, small parameter, monodromy operator. 
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     author = {V. V. Abramov and E. Yu. Liskina},
     title = {On branching of periodic solutions of quasilinear systems of ordinary differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {217},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/}
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V. V. Abramov; E. Yu. Liskina. On branching of periodic solutions of quasilinear systems of ordinary differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/