Rotating periodic solutions in complete degeneracy.

In the present paper, we are concerned with the existence of Q 0 -rotating periodic solutions on a class of perturbed systems in R 2 n. This type of rotating periodic solutions has the form of X (t + T) = Q 0 X (t) , ∀ t ∈ R with T > 0 and Q 0 an orthogonal matrix. The systems under consideration are linear but completely degenerate, in another word, completely resonant. In general it is quite difficult to the situation. We establish a persistence result about Q 0 -rotating periodic solutions undergoing small perturbations. Our transversality condition is based on the topological degree, but easily verifiable in applications. [ABSTRACT FROM AUTHOR]