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 language | English |
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Pages (from-to) | 325-346 |
Number of pages | 22 |
Journal | Collectanea Mathematica |
Volume | 59 |
Issue number | 3 |
DOIs | |
State | Published - 2008 |
Keywords
- Canonical form
- Dynamical system
- Rational map