Additive one-dimensional cellular automata are chaotic according to Devaney's definition of chaos

AbstractWe study the chaotic behavior of a particular class of dynamical systems: cellular automata. We specialize the definition of chaos given by Devaney for general dynamical systems to the case of cellular automata. A dynamical system (X,F) is chaotic according to Devaney's definition of chaos if its transition map F is sensitive to the initial conditions, topologically transitive, and has dense periodic orbits on X. Our main result is the proof that all the additive one-dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of Devaney