TITLE:
Transitivity and Chaoticity in 1-D Cellular Automata
AUTHORS:
Fangyue Chen, Guanrong Chen, Weifeng Jin
KEYWORDS:
Bernoulli Subshift of Finite Type; Cellular Automata; Devaney Chaos; Symbolic Dynamics; Topological Transitivity
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.2 No.1A,
March
29,
2013
ABSTRACT: Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA transitivity but also the CA with transitive non-trivial Bernoulli subshift of finite type have dense periodic points. It is concluded that, for one-dimensional CA, the transitivity implies chaos in the sense of Devaney on the non-trivial Bernoulli subshift of finite types.