2007/09/10 by F. Vivaldi, Franco Vivaldi, Vivaldi, F.
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #math.DS #msc:11Z05 #msc:37F99 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0709.1370
27 pages, 7 postscript figures
arxiv created 2007/09/10 · arxiv updated 2009/12/01
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 g. 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, which affords a fresh viewpoint on some algebraic dynamical constructs. We identify the basic invariant sets, and study in some detail the case of quadratic polynomials. We perform some experiments on self-interacting polynomials over finite fields.