Asymptotic Properties of -Expansive Homeomorphisms on a Metric -Space

Abstract

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