Contents: Finite dynamical systems are given by maps f: X
-> X of a finite set X to itself. One is interested in the behaviour of the iterated maps f^n: X -> X , the dynamic behaviour of the system. Predictions are rather difficult even in the simplest cases. Fixed points and periodic points are of special interest.
There is an extensive literature on maps of the form f: K^n -> K^n, where K is a finite field. All such maps are given by polynomials over K. If f is a linear or affine map, the dynamic behaviour of f can be completely described. If the polynomials describing f are exclusively monomials and K = F_2 then much is known about the fixed points and the periodic points. Such a system may be considered as a Boolean net of AND operators.
Many applications can be found in computer science, bio sciences, traffic control, electric power nets and many other sciences.
We will study special dynamical systems called sequential dynamical systems, where the map f is given by a special construction.