Topological R-entropy and topological entropy of free semigroup actions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Zhu, Li¹  Ma, Dongkui¹ 

[1] South China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

关键词: Topological r-entropy;    Topological entropy;    Free semigroup actions;    Skew-product transformations;   

DOI  :  10.1016/j.jmaa.2018.10.048

来源: Elsevier

【 摘 要 】

We introduce the notion of topological r-entropy for free semigroup actions on a compact metric space and provide some properties of it. By using the skew-product transformation as bridge, we get the following two main results. 1. We extend the result that the topological entropy is the limit of topological r-entropy in [15] to free semigroup actions (r -> 0). 2. Let f(i) i = 0, 1,.., m - 1, be homeomorphisms on a compact metric space. We verify that the topological entropy of f(0),..., f(m-1) equals the topological entropy of f(0)(-1),...,f(m-1)(-1) . (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free