Finite smooth normal forms and integrability of local families of vector fields (Q620008)

From the authors' abstract: A class of smooth vector fields which depend on small parameters and whose eigenvalues may admit certain resonances are studied. Polynomial normal forms for such systems under \(C^k\) conjugacy, where \(k\) can be arbitrarily large, are considered. When the smoothness of normalization is less required, it is showed that these systems can be reduced to their quasi-linearizable normal forms under \(C^{k_0}\) conjugacy, where \(k_0\) is good enough to preserve certain qualitative properties of the original systems while the normal forms are as convenient as the linearized ones in applications.