Geodesic
On the branching of a large periodic solution of a system of differential equations with a parameter
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 3-8.

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We study a normal periodic system of ordinary differential equations with a small parameter, which is quasilinear in a neighborhood of infinity, under the assumption that the right-hand side of the system has a critical linear approximation. In terms of the properties of the first homogeneous nonlinear approximation of the monodromy operator, we obtain conditions for the existence of a periodic solution whose initial value is infinitely large for an infinitesimal value of the parameter.
Keywords: differential equation, periodic solution, small parameter, monodromy operator. 
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V. V. Abramov. On the branching of a large periodic solution of a system of differential equations with a parameter. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 3-8. http://geodesic.mathdoc.fr/item/INTO_2019_168_a0/

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