Vivaldi F.
Self-interacting polynomials
(267K, Postscript)
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.