Periodic solutions of the perturbed symmetric Euler top (Q536508)

Consider the differential system \[ \begin{aligned} {dx\over dt} &=-yz+\varepsilon p(t,x,y,z),\\ {dy\over dt} &= xz+\varepsilon q(t,x,y,k),\\ {dz\over dt} &=\varepsilon s(t,x,y,z),\end{aligned}\tag{\(*\)} \] where \(\varepsilon> 0\) is small and \(p,q,s: \mathbb{R}\times \mathbb{R}^3\times \mathbb{R}\) are continuous functions \(T\)-periodic in the first variable. The authors prove the existence of \(T\)-periodic solutions of \((*)\) for small \(\varepsilon\) bifurcating from a \(T\)-periodic solution of the unperturbed system.