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Dynamical systems for rational normal curves. (English) Zbl 1197.14009

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.

MSC:

14E05 Rational and birational maps
14Q05 Computational aspects of algebraic curves
15A72 Vector and tensor algebra, theory of invariants
92D25 Population dynamics (general)

Software:

Macaulay2
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References:

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