Abstract
A nonlinear non-autonomous system of two ordinary differential equations is considered. It is assumed that the equations corresponding to the principal part in the asymptotics at infinity with respect to the independent variable are integrable and written in the action-angle variables. In the case where the lower terms in the equation periodically depend on the angle, the asymptotic expansion at infinity of the two-parametric family of solutions is constructed.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.
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Kalyakin, L.A. Asymptotics at infinity of solutions of equations close to Hamiltonian equations. J Math Sci 157, 526–542 (2009). https://doi.org/10.1007/s10958-009-9332-3
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DOI: https://doi.org/10.1007/s10958-009-9332-3