Subharmonic bifurcations from normally nonhyperbolic periodic manifolds

A higher dimensional system which has a normally nonhyperbolic periodic manifold is studied in this paper. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two dimensions in normal direction. By using exponential trichotomy, Poincare map and the implicit function theorem, the existence of the subharmonic orbits is given.