ADDITIVE ONE-DIMENSIONAL CELLULAR-AUTOMATA ARE CHAOTIC ACCORDING TO DEVANEYS DEFINITION OF CHAOS

We study the chaotic behavior of a particular class of dynamical syste ms: 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 definitio n of chaos if its transition map F is sensitive to the initial conditi ons, topologically transitive, and has dense peri odic orbits on X. Ou r main result is the proof that all the additive one-dimensional cellu lar automata defined on a finite alphabet of prime cardinality are cha otic in the sense of Devaney.