02-366 Vivaldi F.

Self-interacting polynomials (267K, Postscript) Sep 6, 02

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Abstract. We introduce a class of dynamical systems of algebraic origin, consisting of self-interacting irreducible polynomials over a field. A polynomial $f$ is made to act on a polynomial $g$ by mapping the roots of the latter. This action identifies a new polynomial $h$, as the minimal polynomial of the displaced roots. By allowing several polynomials to act on one another, we obtain a self-interacting system with a rich dynamics and strong collective features, which affords a fresh viewpoint on some algebraic dynamical constructs. We identify the basic dynamical invariants and begin the study of periodic behaviour, organizing the polynomials into an oriented graph.

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