The characterization of degenerate and non-degenerate systems
Let \(x=0\) be a center of the differential equation (1) \(x'=F(x)\). We say that a T-periodic solution u of (1) is non-degenerate if and only if every T-periodic solution of the linear variational equation (2) \(y'=F_ x(u(t))y\) is a multiple of u'(t). The authors use elementary methods to obtain sufficient conditions for every periodic solution of (1) in some neighborhood of the origin to be non-degenerate. The question of non- degeneracy is important in the study of periodic solutions of the weakly perturbed equation (3) \(x'=F(x)+ef(t,x)\) where e is a small parameter.
scientific article; zbMATH DE number 3948791