Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665024 | Advances in Mathematics | 2017 | 31 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Wen Huang, Jian Li, Xiangdong Ye, Xiaoyao Zhou,