G-Strong Chain Recurrent Point and G-Chain Equivalent Point of Topological G-Conjugacy on Metric G-Space

Abstract

In this paper, we study the dynamical properties of G-strong chain recurrent point, G-chain point set and G-chain equivalent point of topological G-conjugacy on metric G-space. By inference, we give the following conclusions that if let f_1: X → X and f_2: Y → Y be two continous map of metric G-space X and Y. Suppose the map h: X → Y is a topogical G-conjugacy from f_1 to f_2, then (1)h(SCR_G ( f_1)) = SCR_G ( f_2 ); (2)h(S_G (x, f_1)) = S_G (h(x), f_2 ); (3)h(CE_G (x, f_1)) = CE_G (h(x), f_2 ). These results will enrich the theory of G-strong chain recurrent point, G-chain point and G-chain equivalent point of topological G-conjugacy on metric G-space.