The complexity of an induced system of Z2-actions

作者：Wu, Qinqi; Zhang, Ruifeng^*

来源：Journal of Differential Equations, 2023, 368: 203-228.

DOI：10.1016/j.jde.2023.05.029

• Entropy
• Family sensitivity
• Induced system

For any minimal system (X, T ) and d > 1, there is an associated minimal system (Nd (X), Gd) introduced by Glasner, where Gd is generated by T x & BULL; & BULL; & BULL; x T and T x T2 x & BULL; & BULL; & BULL; x Td. In this paper, we study the complexity of the induced system. We first show that the induced system (Nd (X), Gd) is null (resp. tame) if and only if so is the original system (X, T ). Moreover, we prove the induced system always has zero topological entropy. Then we study the relationship of the sensitivity between the original system and the induced one. Particularly, we show that (Nd(X), Gd) is thick-sensitive (resp. thickly syndetic-sensitive, IP-sensitive) if and only if so is (X, T ). & COPY; 2023 Elsevier Inc.