Dynamical systems for rational normal curves (Q848652)

The author constructs dynamical systems in \(\mathbb P^n \), using \((n + 1) \times (n + 1)\) matrices of linear forms in \(n + 1\) variables, such that the fixed point sets are rational normal curves minus one point. These matrices provide canonical forms for the triple action of PGL\(_{n+1}\) on the projective space of such matrices. These dynamical systems include parameters identified with points in \(\mathbb P^{n - 1} \). He finds conditions on these parameters to guarantee that any point in a dense open subset of \(\mathbb{P}^n\) converges to a fixed point. He also determines the domain of attraction of every fixed point.