Asymptotic Properties of G -Expansive Homeomorphisms on a Metric G -Space

Abstract

We define and study the notions of positively and negatively $G$-asymptotic points for a homeomorphism on a metric $G$-space. We obtain necessary and sufficient conditions for two points to be positively/negatively $G$-asymptotic. Also, we show that the problem of studying $G$-expansive homeomorphisms on a bounded subset of a normed linear $G$-space is equivalent to the problem of studying linear $G$-expansive homeomorphisms on a bounded subset of another normed linear $G$-space.