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Krylov-Bogolyubov averaging of asymptotically autonomous differential equations |
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| Authors: | Anatoliy Samoilenko Manuel Pinto Sergei Trofimchuk |
| Institution: | Institute of Mathematics, National Academy of Sciences, Tereshchenkyvs'ka str., 3, Kiev, 252601, Ukraine ; Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile ; Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile |
| Abstract: | We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator. |
| Keywords: | Asymptotic integration asymptotically autonomous equation Levinson theorem Krylov-Bogolyubov averaging principle Van-der-Pol oscillator adiabatic oscillator |
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