Equicontinuous Factors of One Dimensional Cellular Automata
We are interested in topological and ergodic properties of one-dimensional cellular automata. We show that an ergodic cellular automaton cannot have irrational eigenvalues. We show that any cellular automaton with an equicontinuous factor has also as a factor an equicontinuous cellular automaton. We show also that a cellular automaton with almost equicontinuous points according to Gilman’s classification has an equicontinuous measurable factor which is a cellular automaton.
Keywords: Irrational eigenvalue, factor of a dynamical system, equicontinuous dynamical system