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periodic system; period map; invariant set; flow
We investigate the nonautonomous periodic system of ODE’s of the form $\dot{x}=\vec{v}(x)+r_{p}(t)(\vec{w}(x)-\vec{v}(x))$, where $r_{p}(t)$ is a $2p$-periodic function defined by $r_{p}(t)=0$ for $t\in \langle 0,p\rangle $, $r_{p}(t)=1$ for $t\in (p,2p)$ and the vector fields $\vec{v}$ and $\vec{w}$ are related by an involutive diffeomorphism.
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