Positive topological entropy and Δ-weakly mixing sets

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• 作者：Wen Huang^a ; ^{wenh@mail.ustc.edu.cn} ; Jian Li^b ; ^{lijian09@mail.ustc.edu.cn} ; Xiangdong Ye^a ; ^{yexd@ustc.edu.cn} ; Xiaoyao Zhou^c ; ^{zhouxiaoyaodeyouxian@126.com}
• 关键词：37B05 ; 37B40 ; 37A35
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：653-683
• 全文大小：556 K
• 卷排序：306

文摘

The notion of Δ-weakly mixing set is introduced and studied. It is proved that Δ-weakly mixing sets share many properties with weakly mixing sets, in particular, if a dynamical system has positive topological entropy, then the collection of Δ-weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace. The existence of Δ-weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. These results generalize several well known results and also answer several open questions.