Point Sets and Periodic Shadowing Property of Topological G-Conjugacy on Metric G-Space

The topological G -conjugacy map has an important significance in terms of theory and application. In this paper, we study recurrent point, non-wandering point and periodic shadowing property of topological G -conjugacy on metric G -space. By means of properties of topological G -conjugacy map and by inference, we will give the following conclusions that if Let f: X → X and t: Y → Y be two continuous map of metric G-space X and Y. Suppose the map h: X → Y is a topogical G -conjugacy from f to t and x2 X, then(1)The point x is a G - recurrent point of f if and only if the point h(x) is a G -recurrent point of t. (2)The point x is a G -nonwandering point of f if and only if the point h(x) is a G -nonwandering point of t. (3) The map f has the G -periodic shadowing property if and only if the map t has the G -periodic shadowing property. These results will enrich the theory of the recurrent point, non-wandering point and periodic shadowing property of topological G -conjugacy on metric G-space.