Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property

• 作者: Peng SUN
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 362-376
• 页数: 15页
• 语种: 英文

摘要

We show that for every topological dynamical system with the approximate product prop-erty, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.