Kůrka, Petr Languages, equicontinuity and attractors in cellular automata. (English) Zbl 0876.68075 Ergodic Theory Dyn. Syst. 17, No. 2, 417-433 (1997). Summary: We consider three related classifications of cellular automata: the first is based on the complexity of languages generated by clopen partitions of the state space, i.e. on the complexity of the factor subshifts; the second is based on the concept of equicontinuity and it is a modification of the classification introduced by R. H. Gilman [ibid. 7, 105-118 (1987; Zbl 0588.68029)]. The third one is based on the concept of attractors and it refines the classification introduced by M. Hurley [\((*)\) ibid. 10, No. 1, 131-140 (1990; Zbl 0666.58029)]. We show relations between these classifications and give examples of cellular automata in the intersection classes. In particular, we show that every positively expansive cellular automaton is conjugate to a one-sided subshift of finite type and that every topologically transitive cellular automaton is sensitive to initial conditions. We also construct a cellular automaton with minimal quasi-attractor, whose basin has measure zero, answering a question raised in \((*)\). Cited in 2 ReviewsCited in 82 Documents MSC: 37B15 Dynamical aspects of cellular automata 68Q80 Cellular automata (computational aspects) Keywords:cellular automata Citations:Zbl 0588.68029; Zbl 0666.58029 PDFBibTeX XMLCite \textit{P. Kůrka}, Ergodic Theory Dyn. Syst. 17, No. 2, 417--433 (1997; Zbl 0876.68075) Full Text: DOI