The equivalent condition of G-asymptotic tracking property and G-Lipschitz tracking property
Copyright policy )The equivalent condition of G-asymptotic tracking property and G-Lipschitz tracking property
Abstract In this paper, we introduce the concepts of G G -Lipschitz tracking property and G G -asymptotic tracking property in metric G G -space and obtain the equivalent conditions of G G -asymptotic tracking property in metric G G -space. In addition, we prove that the self-map f f has the G G -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].
- Wuzhou University China (People's Republic of)
- Guangxi University China (People's Republic of)
metric g-space, g-lipschitz tracking property, Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), 37b99, topological group, \(G\)-Lipschitz tracking property, g-asymptotic tracking property, QA1-939, \(G\)-asymptotic tracking property, Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems, Mathematics, Dynamics in general topological spaces, metric \(G\)-space, inverse limit space
metric g-space, g-lipschitz tracking property, Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), 37b99, topological group, \(G\)-Lipschitz tracking property, g-asymptotic tracking property, QA1-939, \(G\)-asymptotic tracking property, Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems, Mathematics, Dynamics in general topological spaces, metric \(G\)-space, inverse limit space
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