Equivariant nonautonomous normal forms (Q1981910)

For a nonautonomous dynamics with discrete time, the authors show that if the dynamics is equivariant (respectively, reversible), then any normal form, as well as the coordinate change bringing the dynamics into this normal form, have equivariance (respectively, reversibility) properties. They consider dynamics on \(\mathbb{R}^d\) given by \(x_{n+1}=A_nx_n+f_n(x_n)\), where the \(d\times d\)-matrices \(A_n\) are invertible and the maps \(f_n\) are of class \(C^p\), \(p\in \mathbb{N}\). The authors study the relationship between the nonuniform spectrum, the block decomposition of the matrices \(A_n\), the resonances and an explicit construction of the coordinate change which gives the normal form.