Positive topological entropy and $\Delta$-weakly mixing sets
Dynamical Systems
2016-11-08 v1
Abstract
The notion of -weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of -weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace. The existence of -weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. Moreover, Our results generalize several well known results and also answer several open questions.
Cite
@article{arxiv.1504.07520,
title = {Positive topological entropy and $\Delta$-weakly mixing sets},
author = {Wen Huang and Jian Li and Xiangdong Ye and Xiaoyao Zhou},
journal= {arXiv preprint arXiv:1504.07520},
year = {2016}
}
Comments
26 pages