Abstract

We define and study the notion of chain transitivity for maps on $G$-spaces. Through examples we justify that the notion of $G$-chain transitivity depends on the action of $G$. Further, we obtain characterization of $G$-chain transitivity in terms of chain transitivity. A relation between $G$-chain transitivity and $G$-chain recurrent points of a map is also obtained.

Keywords: Chain transitive; chain recurrent points; $G$-space.

MSC: 37C85, 37C50, 37C75, 54H20

Pages:  326--337     

Volume  71 ,  Issue  4 ,  2019