On new resonances and normal forms of autonomous systems with one zero eigenvalue (Q650254)

Consider an autonomous system \[ \dot{\xi}=\frac{d\xi}{dt}=Q(\xi), \] where \(\xi, Q(\xi) \in \mathbb{R}^{n+1}\), \(n>0\), and \(Q\) is a function of class \(C^\infty\) in a neighborhood of the origin, \(Q(0)=0\), and the matrix \(\widetilde{A}=Q'(0)\) has \(n\) eigenvalues lying off the imaginary axis and one zero eigenvalue. The author studies the reduction possibilities of such systems to polynomial normal forms.