Geodesic
On Stability of Small Periodic Solutions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 3-9.

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

In this paper, we consider normal time-periodic systems of ordinary differential equations whose right-hand sides smoothly depend on phase variables and small parameters. Conditions of branching of small periodic solution of the system are found. Stability tests for small Lyapunov solutions with respect to parameters or variables are established. Our reasoning is based on the analysis of the first nonlinear approximation of the monodromy operator.
Keywords: system of ordinary differential equations, small parameter, monodromy operator, branching of a periodic solution, stability. 
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V. V. Abramov. On Stability of Small Periodic Solutions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 3-9. http://geodesic.mathdoc.fr/item/INTO_2018_148_a0/

[1] Abramov V. V., “K voprosu ob ustoichivosti po chasti peremennykh”, Izv. RAEN. Differ. uravn., 16 (2011), 5–8 | MR

[2] Abramov V. V., “Ustoichivost malogo periodicheskogo resheniya”, Vestn. RAEN, 13:4 (2013), 3–5

[3] Abramov V. V., “Dvustoronnyaya ustoichivost malogo periodicheskogo resheniya”, Vest. RAEN, 14:5 (2014), 6–9

[4] Abramov V. V., “Ustoichivost nulevogo resheniya periodicheskoi sistemy differentsialnykh uravnenii s malym parametrom”, Zh. Srednevolzh. mat. o-va, 12:4 (2010), 49–54 | MR | Zbl

[5] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966 | MR

[6] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971

[7] Khapaev M. M., Usrednenie v teorii ustoichivosti, Nauka, M., 1986 | MR