Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study $\Delta$-transitivity, $\Delta$-weak mixing and $\Delta$-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.

Keywords: Semigroup actions, $G$-system, $\Delta$-transitivity, $\Delta$-weak mixing, $\Delta$-mixing

MSC numbers: Primary 37B05; Secondary 54H15

Supported by: The author would like to thank Jian Li and Yini Yang for helpful suggestions. The author was supported by NNSF of China (grant number 12001239) and Guangdong Basic and Applied Basic Research Foundation (2020A1515111113) and YITP of Guangdong Provincial Department of Education of China (grant number 2019KQNCX145).