Multiple-periodic bifurcation and resonance in dynamical systems

We consider finite-dimensional dynamical systems in the presence of real pa rameters, and we want to discuss the existence-under suitable hypotheses-of bifurcating solutions, possibly including multiple-periodic solutions, in correspondence to resonant eigenvalues. The main idea is that to transform the given dynamical system into normal form (in the sense of Poincare-Dulac ) and impose that the normalizing transformation is convergent.