Kurka P.
Dynamical systems and factors of finite automata
(37K, latex)
ABSTRACT. We conceive finite automata as dynamical systems on discontinuum
and investigate their factors. Factors of finite automata include
many well-known simple dynamical systems, e.g. hyperbolic
systems and systems with finite attractors. In the quadratic
family on the real interval, factors of finite automata include
all systems with finite number of periodic points, as well as
systems at the band-merging bifurcations. On the other hand the
system with a non-chaotic attractor, which occurs at the limit of
the period doubling bifurcations (at the edge of chaos), is not
of this class. Next we propose as another simplicity criterion
for dynamical systems the property of having chaotic limits
(every point belongs to a set, whose $\omega$-limit is
chaotic). We show that any factor of a finite automaton has
chaotic limits but not vice versa.