Abstract
We deal with nonlinear periodic differential systems depending on a small parameter. Theunperturbed system has an invariant manifold of periodic solutions. We provide sufficientconditions in order that some of the periodic orbits of this invariant manifold persist after theperturbation. These conditions are not difficult to check, as we show in some applications. Thekey tool for proving the main result is the Lyapunov--Schmidt reduction method applied to thePoincaré--Andronov mapping.
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