Speaker:
Bodo Pareigis, Mathematisches Institut der Universitat Munchen
Title:
Fixed points of finite dynamical systems
Abstract:
Finite dynamical systems f: X > X (time discrete,
finite state space X) occur in many technical applications and
computer science simulations. Despite the finiteness of the
given data, little is known about the dynamical behaviour of
such systems. In particular we are interested in fixed points
and limit cycles (periodic points). For linear maps f: K^n >
K^n for a finite field K fixed points and limit cycles can be
computed from f. We show that they can also be computed for
monomial maps f and the finite field K = Z/2Z. This
computation involves a new graph invariant that can be
determined in polynomial time.
