Abstract
We construct dynamical systems with ℙn as state space, using (n+1)×(n+1) matrices of linear forms inn+1 variables, such that the fixed point sets are rational normal curves minus one point. Our matrices provide canonical forms for the triple action ofPGL n+1 on the projective space of such matrices. Our dynamical systems include parameters identified with points in ℙn −1. We find conditions on these parameters to guarantee that any point in a dense open subset of ℙn converges to a fixed point. We determine the domain of attraction of every fixed point.
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