Dynamical systems for rational normal curves

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Abstract

We construct dynamical systems with Pn as state space, using (n+1)×(n+1) matrices of linear forms in n+1 variables, such that the fixed point sets are rational normal curves minus one point. Our matrices provide canonical forms for the triple action of PGLn+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.

Original languageEnglish
Pages (from-to)325-346
Number of pages22
JournalCollectanea Mathematica
Volume59
Issue number3
DOIs
StatePublished - 2008

Keywords

  • Canonical form
  • Dynamical system
  • Rational map

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