Kurka P.
One-dimensional dynamics and factors of finite automata
(41K, Latex)
ABSTRACT. We argue that simple dynamical systems are factors of finite
automata, regarded as dynamical systems on discontinuum. We show
that any homeomorphism of the real interval is of this class. An
orientation preserving homeomorphism of the circle is a factor of
a finite automaton iff its rotation number is rational.
Any $S$-unimodal system on the real interval, whose kneading
sequence is either periodic odd or preperiodic, is also a factor of a
finite automaton, while $S$-unimodal systems at limits of period
doubling bifurcations are not.