Transitivity and Chaoticity in 1-D Cellular Automata

• 作者: Fangyue Chen Guanrong Chen Weifeng Jin
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: BERNOULLI SUBSHIFT of Finite Type Cellular AUTOMATA Devaney Chaos SYMBOLIC Dynamics TOPOLOGICAL TRANSITIVITY
• 年，卷（期）: 2013,（1）
• 页码范围: 69-73
• 页数: 5页
• 分类号: O1

摘要

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.