Rotating periodic solutions in complete degeneracy (Q2077100)

In this paper, the authors study the existence of \(Q_0\)-rotating periodic solutions on a class of perturbed systems in \(\mathbb{R}^n\). This kind of rotating periodic solutions has the from of \(X(t+T)=Q_0X(t)\) \(\forall t\in \mathbb{R}\) with \(T>0\) and \(Q_0\) an orthogonal matrix. The systems under consideration are linear but completely degenerate. When the linear systems take small perturbations, the authors prove the existence of \(Q_0\)-rotating periodic solutions for the given systems by using the topological degree theory.