Finite smooth normal forms and integrability of local families of vector fields
Finite smooth normal forms and integrability of local families of vector fields
In this paper we study a class of smooth vector fields which depend on small parameters and their eigenvalues may admit certain resonances. We shall derive the polynomial normal forms for such systems under $C^k$ conjugacy, where $k$ can be arbitrarily large. When the smoothness of normalization is less required, …