The equivalent condition of G-asymptotic tracking property and G-Lipschitz tracking property

Abstract

In this paper, we introduce the concepts of GG-Lipschitz tracking property and GG-asymptotic tracking property in metric GG-space and obtain the equivalent conditions of GG-asymptotic tracking property in metric GG-space. In addition, we prove that the self-map ff has the GG-Lipschitz tracking property if and only if the shift map σ\sigma has the G¯\overline{G}-Lipschitz tracking property in the inverse limit space under the topological group action. These results generalize the corresponding results in [Proc. Amer. Math. Soc. 115 (1992), 573–580].

Keywords

• metric g-space
• topological group
• inverse limit space
• g-lipschitz tracking property
• g-asymptotic tracking property
• 37b99